This version of the adiposity analysis mirrors the birth weight analysis from 09_NPB_Model_BW_v4_MD.R

Some key findings to note:

  • There are fewer participants with complete data on the adiposity outcome and covariates of interest
  • Update 02-10-21: Adding a sensitivity analysis where I exclude race/ethnicity (since it might be a mediator)

1 Exploring the data set

The HS data set was previously used in the CEI paper (Martenies et al., 2019). In the original analysis, we used an exposure index based on the CalEnvironScreen tool. We observed lower birth weights and lower adiposity associated with higher index scores, driven largely by exposures to social indicators of health at the neighborhood level. Now, we are aiming to use methods for mixtures to try to identify which exposures are driving these association.

The complete data set for the adiposity outcome consists of n = 780 participants. This represents 67.77% of the original Healthy Start 1 cohort.

Of the 780 participants, 0.26% identify as Latina, 0.17% identify as Black, and 0.26% identify as another non-NHW race or ethnicity. The median age of mothers in this dataset is 28 years. 0.51% of babies born were male.

1.1 Exposure data

We have included 20 exposures in our analysis.

These exposures are based on the census tract where each mother lived at the time of enrollment into Healthy Start. With the exception of air pollution (mean_pm and mean_o3), these are based on long-term averages at for each census tract. For mean_pm and mean_o3 are based on the average pollution levels across each pregnancy (est. conception date to delivery date) estimated using ordinary kriging and monitoring data.

#' Exposure data
X <- select(hs_data2, mean_pm, mean_o3, mean_temp, pct_tree_cover, pct_impervious,
            mean_aadt_intensity, dist_m_tri:dist_m_mine_well,
            cvd_rate_adj, res_rate_adj, violent_crime_rate, property_crime_rate,
            pct_less_hs, pct_unemp, pct_limited_eng, pct_hh_pov, pct_poc) %>%
  as.matrix()
head(X)
##       mean_pm  mean_o3 mean_temp pct_tree_cover pct_impervious
## [1,] 8.483046 47.19072  51.81487       6.006276       43.30893
## [2,] 6.598608 50.05090  58.32885       7.281109       48.36432
## [3,] 7.454146 48.57052  58.01924      17.205991       31.67281
## [4,] 6.671239 50.06429  61.35590       6.842898       45.00359
## [5,] 7.122537 50.14275  59.28421       3.357792       28.16745
## [6,] 7.637453 47.03125  55.32825      10.743612       45.87564
##      mean_aadt_intensity dist_m_tri dist_m_npl dist_m_waste_site
## [1,]          10128.4962   2827.538   729.2371          4829.780
## [2,]          10749.0359   1576.420  5239.2211          4417.792
## [3,]           9048.6468   3350.303  2992.2968          5211.871
## [4,]           4223.3434   3364.954  6998.1286          8921.318
## [5,]            858.7283   2923.811  3427.2247          7006.042
## [6,]          15603.9800   3364.200  3166.5395          4484.960
##      dist_m_major_emit dist_m_cafo dist_m_mine_well cvd_rate_adj res_rate_adj
## [1,]          7968.654    29116.58        1749.1256     275.2480     155.7767
## [2,]          3780.951    51044.30        7354.5310     279.6435     226.8038
## [3,]          7423.232    36079.21        4887.2996     221.0414     157.6974
## [4,]          9636.816    42235.78        3752.6399     203.8812     142.5368
## [5,]          6806.912    29145.98         729.7784     194.1983     101.0046
## [6,]          5265.285    43921.85        5870.6867     174.3361     120.3281
##      violent_crime_rate property_crime_rate pct_less_hs pct_unemp
## [1,]          14.377133            37.32935   31.784946 11.529628
## [2,]           8.905404            67.03932   15.290231  4.908306
## [3,]           7.636888            46.78194    6.891702  4.564963
## [4,]           2.850212            21.95270    2.725915  5.623583
## [5,]           5.435988            22.49834   12.919186  5.234103
## [6,]           5.035971            47.15500    3.842365 10.000000
##      pct_limited_eng pct_hh_pov  pct_poc
## [1,]       26.114650  12.010919 90.33703
## [2,]        8.500401  18.123496 30.44025
## [3,]        0.000000   6.307978 26.63305
## [4,]        1.350621   9.292274 32.68648
## [5,]        6.307385   2.115768 73.60772
## [6,]        5.121799  25.171768 23.08698

Variance and histograms of the exposure variables (in their original units):

var(X)
##                             mean_pm        mean_o3     mean_temp pct_tree_cover
## mean_pm                 0.387935651   -0.006062324    0.08159322    -0.24186797
## mean_o3                -0.006062324    8.955071063   10.91751296    -0.42975173
## mean_temp               0.081593216   10.917512965   19.07709741     0.42247728
## pct_tree_cover         -0.241867968   -0.429751728    0.42247728    10.14239201
## pct_impervious          0.374669222   -1.022666581    4.17459123     7.01532904
## mean_aadt_intensity  -244.348900205  303.692966735 2560.03377531  9016.25164719
## dist_m_tri           -262.436608185  331.077954338 -912.79043355  -208.41963901
## dist_m_npl           -323.917936386  588.917794378 -131.31485219   165.47445225
## dist_m_waste_site    -255.868380544  139.101947771 -108.57465114  1967.86242644
## dist_m_major_emit      54.696478097  795.943835213  362.18792432   109.80052618
## dist_m_cafo         -1416.446418998 -161.908280851  105.15291800 10579.76974425
## dist_m_mine_well     -346.805134977 -503.738613039 -365.87801373  3305.89212551
## cvd_rate_adj            3.764074301    4.075840732   10.83290159   -24.37524733
## res_rate_adj            1.965274289    1.428149656    9.57543380    -1.41491470
## violent_crime_rate      0.155877411    0.749569861    1.11397496    -3.73949960
## property_crime_rate     1.705778861   -1.922286944    5.72267156   -21.72665992
## pct_less_hs             1.150349004    1.853281484    1.91377595    -7.56529205
## pct_unemp               0.055091002    0.506543293    0.44701628    -0.09840703
## pct_limited_eng         0.412512233    1.029344921    0.81158219    -2.79407307
## pct_hh_pov              0.606596961    0.246447334    1.69567408     0.62423227
## pct_poc                 1.697984717    3.441448054    2.04851012   -19.39024560
##                     pct_impervious mean_aadt_intensity    dist_m_tri
## mean_pm                  0.3746692           -244.3489     -262.4366
## mean_o3                 -1.0226666            303.6930      331.0780
## mean_temp                4.1745912           2560.0338     -912.7904
## pct_tree_cover           7.0153290           9016.2516     -208.4196
## pct_impervious         179.3785613          56186.2650   -16125.7853
## mean_aadt_intensity  56186.2649588       69165922.5363 -1545741.2032
## dist_m_tri          -16125.7853155       -1545741.2032  6796986.1348
## dist_m_npl           -9073.4066413        1215685.3718  4579262.3957
## dist_m_waste_site    -5149.3668557        1813109.3670  2501094.5398
## dist_m_major_emit     2552.7325419        2477044.2166  1636072.5435
## dist_m_cafo          17731.4297754       15642123.4910  3145985.3646
## dist_m_mine_well      1088.8996239        2146886.0916   937920.3657
## cvd_rate_adj           238.2585184          20288.9695   -51713.8246
## res_rate_adj           182.9073227          34962.3596   -32708.1468
## violent_crime_rate      23.5426763           4766.3910     -848.4942
## property_crime_rate     96.9554914          18227.6819    -3222.6487
## pct_less_hs             59.7110274          -3644.3902   -12701.6695
## pct_unemp               25.7808764           5880.6527    -2452.4569
## pct_limited_eng         42.8626714           2701.0340    -5437.8035
## pct_hh_pov              84.0422503          18597.5270    -8881.9880
## pct_poc                 89.6891621           4493.4912   -18654.6550
##                        dist_m_npl dist_m_waste_site dist_m_major_emit
## mean_pm                 -323.9179         -255.8684          54.69648
## mean_o3                  588.9178          139.1019         795.94384
## mean_temp               -131.3149         -108.5747         362.18792
## pct_tree_cover           165.4745         1967.8624         109.80053
## pct_impervious         -9073.4066        -5149.3669        2552.73254
## mean_aadt_intensity  1215685.3718      1813109.3670     2477044.21655
## dist_m_tri           4579262.3957      2501094.5398     1636072.54352
## dist_m_npl          11347069.4851      4199731.9447     7041775.87881
## dist_m_waste_site    4199731.9447      5299321.7913     1350703.22559
## dist_m_major_emit    7041775.8788      1350703.2256    10385263.63290
## dist_m_cafo          4931146.1458      5617993.1230    -3395813.15490
## dist_m_mine_well      258232.8698      1384614.0282    -1787310.96945
## cvd_rate_adj          -33265.8693       -43188.0097       15096.48910
## res_rate_adj          -19718.2591       -31937.2229       -1526.60012
## violent_crime_rate      -152.7587        -3204.3439         461.39386
## property_crime_rate   -14876.4444       -19362.3191      -20045.85330
## pct_less_hs            -6945.0281       -11539.8973        8548.88251
## pct_unemp               2139.2957        -1457.5039        5159.73353
## pct_limited_eng          432.5398        -4292.4445        9331.34328
## pct_hh_pov             -1451.6169        -7730.1917        8680.72868
## pct_poc                -2074.8078        -8515.4005       21998.02980
##                       dist_m_cafo dist_m_mine_well  cvd_rate_adj  res_rate_adj
## mean_pm                -1416.4464        -346.8051      3.764074      1.965274
## mean_o3                 -161.9083        -503.7386      4.075841      1.428150
## mean_temp                105.1529        -365.8780     10.832902      9.575434
## pct_tree_cover         10579.7697        3305.8921    -24.375247     -1.414915
## pct_impervious         17731.4298        1088.8996    238.258518    182.907323
## mean_aadt_intensity 15642123.4910     2146886.0916  20288.969539  34962.359641
## dist_m_tri           3145985.3646      937920.3657 -51713.824619 -32708.146822
## dist_m_npl           4931146.1458      258232.8698 -33265.869348 -19718.259098
## dist_m_waste_site    5617993.1230     1384614.0282 -43188.009668 -31937.222912
## dist_m_major_emit   -3395813.1549    -1787310.9695  15096.489101  -1526.600117
## dist_m_cafo         46839423.7820     9553723.7226 -44601.199501  -7797.531774
## dist_m_mine_well     9553723.7226     4464054.8852 -38076.395520 -14953.132358
## cvd_rate_adj          -44601.1995      -38076.3955   2076.657134   1315.804108
## res_rate_adj           -7797.5318      -14953.1324   1315.804108   1110.806026
## violent_crime_rate       408.3455       -2058.0613    134.891314    100.535111
## property_crime_rate   -18380.9466       -4567.0382    320.604924    290.157212
## pct_less_hs           -24463.8379       -9889.2545    334.637464    201.489440
## pct_unemp               -416.0610       -2620.4519    105.334428     74.963887
## pct_limited_eng        -6285.3923       -4618.3890    185.226339    106.490953
## pct_hh_pov               252.0453       -4667.4525    269.033064    206.556606
## pct_poc               -42540.4506      -24578.3527    619.542560    300.056264
##                     violent_crime_rate property_crime_rate   pct_less_hs
## mean_pm                      0.1558774            1.705779      1.150349
## mean_o3                      0.7495699           -1.922287      1.853281
## mean_temp                    1.1139750            5.722672      1.913776
## pct_tree_cover              -3.7394996          -21.726660     -7.565292
## pct_impervious              23.5426763           96.955491     59.711027
## mean_aadt_intensity       4766.3910356        18227.681901  -3644.390223
## dist_m_tri                -848.4941529        -3222.648703 -12701.669456
## dist_m_npl                -152.7586849       -14876.444381  -6945.028107
## dist_m_waste_site        -3204.3438644       -19362.319083 -11539.897288
## dist_m_major_emit          461.3938611       -20045.853299   8548.882507
## dist_m_cafo                408.3455047       -18380.946611 -24463.837868
## dist_m_mine_well         -2058.0613390        -4567.038163  -9889.254521
## cvd_rate_adj               134.8913140          320.604924    334.637464
## res_rate_adj               100.5351114          290.157212    201.489440
## violent_crime_rate          36.5195077          135.346154     25.285073
## property_crime_rate        135.3461545         1160.236223      3.004961
## pct_less_hs                 25.2850735            3.004961    163.762734
## pct_unemp                   12.0566338            3.018063     40.254624
## pct_limited_eng             14.1433364          -11.409839     86.491751
## pct_hh_pov                  30.5537434           63.667397    103.102830
## pct_poc                     52.0085020          -26.369164    241.514049
##                          pct_unemp pct_limited_eng    pct_hh_pov       pct_poc
## mean_pm                 0.05509100       0.4125122     0.6065970      1.697985
## mean_o3                 0.50654329       1.0293449     0.2464473      3.441448
## mean_temp               0.44701628       0.8115822     1.6956741      2.048510
## pct_tree_cover         -0.09840703      -2.7940731     0.6242323    -19.390246
## pct_impervious         25.78087638      42.8626714    84.0422503     89.689162
## mean_aadt_intensity  5880.65274910    2701.0340348 18597.5269669   4493.491248
## dist_m_tri          -2452.45686782   -5437.8034938 -8881.9879579 -18654.655039
## dist_m_npl           2139.29571806     432.5397585 -1451.6169481  -2074.807832
## dist_m_waste_site   -1457.50390263   -4292.4445272 -7730.1916796  -8515.400484
## dist_m_major_emit    5159.73353103    9331.3432771  8680.7286763  21998.029803
## dist_m_cafo          -416.06100829   -6285.3922771   252.0452517 -42540.450615
## dist_m_mine_well    -2620.45185414   -4618.3890431 -4667.4524666 -24578.352704
## cvd_rate_adj          105.33442831     185.2263391   269.0330637    619.542560
## res_rate_adj           74.96388699     106.4909525   206.5566058    300.056264
## violent_crime_rate     12.05663378      14.1433364    30.5537434     52.008502
## property_crime_rate     3.01806326     -11.4098394    63.6673970    -26.369164
## pct_less_hs            40.25462427      86.4917511   103.1028300    241.514049
## pct_unemp              24.70089342      25.8002340    37.9257486     73.691783
## pct_limited_eng        25.80023399      69.4638469    69.0402541    143.757101
## pct_hh_pov             37.92574856      69.0402541   122.9753676    158.037277
## pct_poc                73.69178348     143.7571008   158.0372769    530.391699
ggplot(pivot_longer(as.data.frame(X), mean_pm:pct_poc, names_to = "exp", values_to = "value")) + 
    geom_histogram(aes(x = value)) + 
    facet_wrap(~ exp, scales = "free")
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

Scaling the exposure variables

X.scaled <- apply(X, 2, scale)
head(X.scaled)
##          mean_pm    mean_o3  mean_temp pct_tree_cover pct_impervious
## [1,]  1.63895222 -0.2235917 -0.1608519    -0.09106707      0.2355128
## [2,] -1.38658135  0.7321879  1.3305352     0.30923073      0.6129716
## [3,] -0.01298527  0.2374938  1.2596504     3.42564459     -0.6332930
## [4,] -1.26996939  0.7366655  2.0235840     0.17163233      0.3620440
## [5,] -0.54539411  0.7628814  1.5492657    -0.92269126     -0.8950193
## [6,]  0.28132089 -0.2768817  0.6435419     1.39645679      0.4271554
##      mean_aadt_intensity dist_m_tri  dist_m_npl dist_m_waste_site
## [1,]        -0.004372722 -0.3966655 -1.41524068      -0.158944386
## [2,]         0.070241827 -0.8765539 -0.07638689      -0.337912010
## [3,]        -0.134215290 -0.1961498 -0.74341877       0.007035929
## [4,]        -0.714416377 -0.1905302  0.44577016       1.618419775
## [5,]        -1.118982302 -0.3597382 -0.61430417       0.786424074
## [6,]         0.654006942 -0.1908194 -0.69169232      -0.308734136
##      dist_m_major_emit dist_m_cafo dist_m_mine_well cvd_rate_adj res_rate_adj
## [1,]       -0.09829063  -1.1211055       -0.7694006    0.6888535   -0.2667071
## [2,]       -1.39776302   2.0828583        1.8836300    0.7853085    1.8643986
## [3,]       -0.26753873  -0.1037626        0.7158928   -0.5006603   -0.2090789
## [4,]        0.41935153   0.7958031        0.1788599   -0.8772257   -0.6639585
## [5,]       -0.45878682  -1.1168106       -1.2518563   -1.0897090   -1.9100974
## [6,]       -0.93716429   1.0421630        1.1813285   -1.5255654   -1.3303122
##      violent_crime_rate property_crime_rate pct_less_hs   pct_unemp
## [1,]          0.2857705          -0.5116110  1.20006290  0.38269452
## [2,]         -0.6196746           0.3606149 -0.08889067 -0.94956352
## [3,]         -0.8295849          -0.2341017 -0.74518055 -1.01864671
## [4,]         -1.6216694          -0.9630391 -1.07070943 -0.80564470
## [5,]         -1.1937830          -0.9470203 -0.27417225 -0.88401077
## [6,]         -1.2599766          -0.2231493 -0.98346622  0.07492226
##      pct_limited_eng pct_hh_pov    pct_poc
## [1,]      2.15729293 -0.2815741  1.5763100
## [2,]      0.04387831  0.2696336 -1.0244789
## [3,]     -0.97602734 -0.7958425 -1.1897923
## [4,]     -0.81397542 -0.5267306 -0.9269452
## [5,]     -0.21924683 -1.1738791  0.8499036
## [6,]     -0.36149732  0.9052185 -1.3437665

Variance and histograms of the exposure variables (scaled):

var(X.scaled)
##                          mean_pm      mean_o3    mean_temp pct_tree_cover
## mean_pm              1.000000000 -0.003252556  0.029992872   -0.121934980
## mean_o3             -0.003252556  1.000000000  0.835281859   -0.045093393
## mean_temp            0.029992872  0.835281859  1.000000000    0.030372253
## pct_tree_cover      -0.121934980 -0.045093393  0.030372253    1.000000000
## pct_impervious       0.044914121 -0.025516099  0.071362908    0.164472230
## mean_aadt_intensity -0.047172018  0.012202649  0.070476359    0.340415825
## dist_m_tri          -0.161616753  0.042436304 -0.080159821   -0.025102111
## dist_m_npl          -0.154387912  0.058422253 -0.008925157    0.015424777
## dist_m_waste_site   -0.178454140  0.020192428 -0.010798468    0.268419703
## dist_m_major_emit    0.027250266  0.082535188  0.025731734    0.010698563
## dist_m_cafo         -0.332287904 -0.007905490  0.003517705    0.485400532
## dist_m_mine_well    -0.263536583 -0.079672044 -0.039647463    0.491307868
## cvd_rate_adj         0.132616005  0.029888236  0.054425979   -0.167956353
## res_rate_adj         0.094672580  0.014319244  0.065778383   -0.013330331
## violent_crime_rate   0.041413399  0.041449103  0.042204312   -0.194303596
## property_crime_rate  0.080402522 -0.018858645  0.038465330   -0.200285524
## pct_less_hs          0.144325222  0.048394870  0.034239499   -0.185629913
## pct_unemp            0.017796906  0.034058516  0.020592585   -0.006217268
## pct_limited_eng      0.079465308  0.041271190  0.022294459   -0.105266007
## pct_hh_pov           0.087823617  0.007426438  0.035008795    0.017675307
## pct_poc              0.118373795  0.049935378  0.020364962   -0.264371573
##                     pct_impervious mean_aadt_intensity  dist_m_tri   dist_m_npl
## mean_pm                 0.04491412         -0.04717202 -0.16161675 -0.154387912
## mean_o3                -0.02551610          0.01220265  0.04243630  0.058422253
## mean_temp               0.07136291          0.07047636 -0.08015982 -0.008925157
## pct_tree_cover          0.16447223          0.34041583 -0.02510211  0.015424777
## pct_impervious          1.00000000          0.50442756 -0.46182497 -0.201114438
## mean_aadt_intensity     0.50442756          1.00000000 -0.07129064  0.043394356
## dist_m_tri             -0.46182497         -0.07129064  1.00000000  0.521429359
## dist_m_npl             -0.20111444          0.04339436  0.52142936  1.000000000
## dist_m_waste_site      -0.16701613          0.09470388  0.41673672  0.541588668
## dist_m_major_emit       0.05914408          0.09242275  0.19473123  0.648681599
## dist_m_cafo             0.19344287          0.27481716  0.17631641  0.213894809
## dist_m_mine_well        0.03848024          0.12217945  0.17027191  0.036283143
## cvd_rate_adj            0.39037390          0.05353422 -0.43527735 -0.216707839
## res_rate_adj            0.40975731          0.12613498 -0.37642515 -0.175633598
## violent_crime_rate      0.29087615          0.09483772 -0.05385527 -0.007504152
## property_crime_rate     0.21252691          0.06434461 -0.03628955 -0.129653449
## pct_less_hs             0.34838683         -0.03424296 -0.38071069 -0.161110784
## pct_unemp               0.38730765          0.14227321 -0.18927221  0.127782869
## pct_limited_eng         0.38398526          0.03896768 -0.25025681  0.015406527
## pct_hh_pov              0.56585263          0.20165084 -0.30721536 -0.038859849
## pct_poc                 0.29077451          0.02346062 -0.31069243 -0.026744696
##                     dist_m_waste_site dist_m_major_emit  dist_m_cafo
## mean_pm                   -0.17845414        0.02725027 -0.332287904
## mean_o3                    0.02019243        0.08253519 -0.007905490
## mean_temp                 -0.01079847        0.02573173  0.003517705
## pct_tree_cover             0.26841970        0.01069856  0.485400532
## pct_impervious            -0.16701613        0.05914408  0.193442865
## mean_aadt_intensity        0.09470388        0.09242275  0.274817163
## dist_m_tri                 0.41673672        0.19473123  0.176316410
## dist_m_npl                 0.54158867        0.64868160  0.213894809
## dist_m_waste_site          1.00000000        0.18207111  0.356586819
## dist_m_major_emit          0.18207111        1.00000000 -0.153967569
## dist_m_cafo                0.35658682       -0.15396757  1.000000000
## dist_m_mine_well           0.28467794       -0.26249836  0.660696709
## cvd_rate_adj              -0.41169031        0.10279803 -0.143007353
## res_rate_adj              -0.41626308       -0.01421338 -0.034184739
## violent_crime_rate        -0.23033849        0.02369194  0.009873237
## property_crime_rate       -0.24693009       -0.18261758 -0.078847675
## pct_less_hs               -0.39172768        0.20729701 -0.279325946
## pct_unemp                 -0.12739232        0.32215300 -0.012231928
## pct_limited_eng           -0.22372532        0.34742094 -0.110191273
## pct_hh_pov                -0.30281059        0.24290606  0.003320960
## pct_poc                   -0.16061887        0.29639895 -0.269896936
##                     dist_m_mine_well cvd_rate_adj res_rate_adj
## mean_pm                  -0.26353658   0.13261601   0.09467258
## mean_o3                  -0.07967204   0.02988824   0.01431924
## mean_temp                -0.03964746   0.05442598   0.06577838
## pct_tree_cover            0.49130787  -0.16795635  -0.01333033
## pct_impervious            0.03848024   0.39037390   0.40975731
## mean_aadt_intensity       0.12217945   0.05353422   0.12613498
## dist_m_tri                0.17027191  -0.43527735  -0.37642515
## dist_m_npl                0.03628314  -0.21670784  -0.17563360
## dist_m_waste_site         0.28467794  -0.41169031  -0.41626308
## dist_m_major_emit        -0.26249836   0.10279803  -0.01421338
## dist_m_cafo               0.66069671  -0.14300735  -0.03418474
## dist_m_mine_well          1.00000000  -0.39546556  -0.21234806
## cvd_rate_adj             -0.39546556   1.00000000   0.86634271
## res_rate_adj             -0.21234806   0.86634271   1.00000000
## violent_crime_rate       -0.16118740   0.48982295   0.49915588
## property_crime_rate      -0.06345950   0.20654495   0.25558834
## pct_less_hs              -0.36575582   0.57383181   0.47241713
## pct_unemp                -0.24954857   0.46508423   0.45256051
## pct_limited_eng          -0.26226862   0.48768672   0.38336652
## pct_hh_pov               -0.19920768   0.53237076   0.55887015
## pct_poc                  -0.50511428   0.59032393   0.39091760
##                     violent_crime_rate property_crime_rate pct_less_hs
## mean_pm                    0.041413399          0.08040252  0.14432522
## mean_o3                    0.041449103         -0.01885865  0.04839487
## mean_temp                  0.042204312          0.03846533  0.03423950
## pct_tree_cover            -0.194303596         -0.20028552 -0.18562991
## pct_impervious             0.290876145          0.21252691  0.34838683
## mean_aadt_intensity        0.094837724          0.06434461 -0.03424296
## dist_m_tri                -0.053855270         -0.03628955 -0.38071069
## dist_m_npl                -0.007504152         -0.12965345 -0.16111078
## dist_m_waste_site         -0.230338488         -0.24693009 -0.39172768
## dist_m_major_emit          0.023691938         -0.18261758  0.20729701
## dist_m_cafo                0.009873237         -0.07884767 -0.27932595
## dist_m_mine_well          -0.161187402         -0.06345950 -0.36575582
## cvd_rate_adj               0.489822949          0.20654495  0.57383181
## res_rate_adj               0.499155881          0.25558834  0.47241713
## violent_crime_rate         1.000000000          0.65752195  0.32695970
## property_crime_rate        0.657521947          1.00000000  0.00689379
## pct_less_hs                0.326959697          0.00689379  1.00000000
## pct_unemp                  0.401427649          0.01782784  0.63292450
## pct_limited_eng            0.280808338         -0.04019082  0.81093815
## pct_hh_pov                 0.455924473          0.16855235  0.72653072
## pct_poc                    0.373691766         -0.03361436  0.81947649
##                        pct_unemp pct_limited_eng   pct_hh_pov     pct_poc
## mean_pm              0.017796906      0.07946531  0.087823617  0.11837380
## mean_o3              0.034058516      0.04127119  0.007426438  0.04993538
## mean_temp            0.020592585      0.02229446  0.035008795  0.02036496
## pct_tree_cover      -0.006217268     -0.10526601  0.017675307 -0.26437157
## pct_impervious       0.387307652      0.38398526  0.565852631  0.29077451
## mean_aadt_intensity  0.142273206      0.03896768  0.201650845  0.02346062
## dist_m_tri          -0.189272211     -0.25025681 -0.307215358 -0.31069243
## dist_m_npl           0.127782869      0.01540653 -0.038859849 -0.02674470
## dist_m_waste_site   -0.127392321     -0.22372532 -0.302810585 -0.16061887
## dist_m_major_emit    0.322153000      0.34742094  0.242906063  0.29639895
## dist_m_cafo         -0.012231928     -0.11019127  0.003320960 -0.26989694
## dist_m_mine_well    -0.249548573     -0.26226862 -0.199207679 -0.50511428
## cvd_rate_adj         0.465084229      0.48768672  0.532370759  0.59032393
## res_rate_adj         0.452560508      0.38336652  0.558870145  0.39091760
## violent_crime_rate   0.401427649      0.28080834  0.455924473  0.37369177
## property_crime_rate  0.017827843     -0.04019082  0.168552353 -0.03361436
## pct_less_hs          0.632924498      0.81093815  0.726530718  0.81947649
## pct_unemp            1.000000000      0.62285635  0.688127265  0.64381987
## pct_limited_eng      0.622856353      1.00000000  0.746988474  0.74894777
## pct_hh_pov           0.688127265      0.74698847  1.000000000  0.61880258
## pct_poc              0.643819872      0.74894777  0.618802578  1.00000000
ggplot(pivot_longer(as.data.frame(X.scaled), mean_pm:pct_poc, 
                    names_to = "exp", values_to = "value")) + 
    geom_histogram(aes(x = value)) + 
    facet_wrap(~ exp, scales = "free")
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

1.2 Covariate data

Covariates were assessed at the individual level. These were selected based on previous HS studies and others in the literature and informed by a DAG.

There are four continuous covariates; all of the others have been coded as dummy variables. For the dummy variables, the reference groups are: white_re, ed_grad, norm_bmi

W <- select(hs_data2, 
            lat, lon, lat_lon_int,
            latina_re, black_re, other_re,
            ed_no_hs, ed_hs, ed_aa, ed_4yr,
            low_bmi, ovwt_bmi, obese_bmi,
            concep_spring, concep_summer, concep_fall,
            concep_2010, concep_2011, concep_2012, concep_2013,
            maternal_age, any_smoker, smokeSH, mean_cpss, mean_epsd,
            male, gest_age_w, days_to_peapod) %>%
  as.matrix()
head(W)
##           lat       lon lat_lon_int latina_re black_re other_re ed_no_hs ed_hs
## [1,] 39.79402 -104.8133   -4170.944         1        0        0        0     0
## [2,] 39.62671 -104.9927   -4160.517         0        0        1        0     0
## [3,] 39.74934 -104.9129   -4170.219         0        0        0        0     0
## [4,] 39.68397 -104.8933   -4162.583         0        0        0        0     0
## [5,] 39.79134 -104.7669   -4168.814         0        1        0        0     0
## [6,] 39.68050 -104.9451   -4164.274         1        0        0        0     0
##      ed_aa ed_4yr low_bmi ovwt_bmi obese_bmi concep_spring concep_summer
## [1,]     1      0       0        0         0             0             0
## [2,]     1      0       0        0         0             0             0
## [3,]     0      0       0        0         0             0             0
## [4,]     1      0       0        0         0             1             0
## [5,]     0      1       0        0         0             1             0
## [6,]     1      0       0        0         0             0             0
##      concep_fall concep_2010 concep_2011 concep_2012 concep_2013 maternal_age
## [1,]           0           0           0           0           0           19
## [2,]           0           1           0           0           0           36
## [3,]           0           1           0           0           0           34
## [4,]           0           1           0           0           0           28
## [5,]           0           1           0           0           0           30
## [6,]           0           1           0           0           0           22
##      any_smoker smokeSH mean_cpss mean_epsd male gest_age_w days_to_peapod
## [1,]          0       1        29         0    0   40.57143              1
## [2,]          0       0        19         2    1   35.85714              2
## [3,]          0       0        19         1    0   40.42857              2
## [4,]          0       0        20         0    0   36.28571              1
## [5,]          0       0        15         0    1   38.42857              2
## [6,]          0       0        17         1    0   40.71429              1

Scaled the non-binary (continuous) covariates

colnames(W)
##  [1] "lat"            "lon"            "lat_lon_int"    "latina_re"     
##  [5] "black_re"       "other_re"       "ed_no_hs"       "ed_hs"         
##  [9] "ed_aa"          "ed_4yr"         "low_bmi"        "ovwt_bmi"      
## [13] "obese_bmi"      "concep_spring"  "concep_summer"  "concep_fall"   
## [17] "concep_2010"    "concep_2011"    "concep_2012"    "concep_2013"   
## [21] "maternal_age"   "any_smoker"     "smokeSH"        "mean_cpss"     
## [25] "mean_epsd"      "male"           "gest_age_w"     "days_to_peapod"
W.s <- apply(W[,c(1, 2, 3, 21, 24, 25, 27, 28)], 2, scale) #' just the continuous ones

W.scaled <- cbind(W.s[,1:3],
                  W[,4:20], W.s[,4],
                  W[,22:23], W.s[,5:6],
                  W[,26], W.s[,7:8])
colnames(W.scaled)
##  [1] "lat"            "lon"            "lat_lon_int"    "latina_re"     
##  [5] "black_re"       "other_re"       "ed_no_hs"       "ed_hs"         
##  [9] "ed_aa"          "ed_4yr"         "low_bmi"        "ovwt_bmi"      
## [13] "obese_bmi"      "concep_spring"  "concep_summer"  "concep_fall"   
## [17] "concep_2010"    "concep_2011"    "concep_2012"    "concep_2013"   
## [21] ""               "any_smoker"     "smokeSH"        "mean_cpss"     
## [25] "mean_epsd"      ""               "gest_age_w"     "days_to_peapod"
colnames(W.scaled) <- colnames(W)
head(W.scaled)
##             lat        lon lat_lon_int latina_re black_re other_re ed_no_hs
## [1,]  0.9582490  0.5369709  -0.5836483         1        0        0        0
## [2,] -1.5595136 -1.6096907   0.6608980         0        0        1        0
## [3,]  0.2858292 -0.6547167  -0.4971411         0        0        0        0
## [4,] -0.6978905 -0.4200223   0.4143032         0        0        0        0
## [5,]  0.9178908  1.0931096  -0.3293688         0        1        0        0
## [6,] -0.7500299 -1.0397812   0.2123849         1        0        0        0
##      ed_hs ed_aa ed_4yr low_bmi ovwt_bmi obese_bmi concep_spring concep_summer
## [1,]     0     1      0       0        0         0             0             0
## [2,]     0     1      0       0        0         0             0             0
## [3,]     0     0      0       0        0         0             0             0
## [4,]     0     1      0       0        0         0             1             0
## [5,]     0     0      1       0        0         0             1             0
## [6,]     0     1      0       0        0         0             0             0
##      concep_fall concep_2010 concep_2011 concep_2012 concep_2013 maternal_age
## [1,]           0           0           0           0           0  -1.41994612
## [2,]           0           1           0           0           0   1.35302672
## [3,]           0           1           0           0           0   1.02679462
## [4,]           0           1           0           0           0   0.04809832
## [5,]           0           1           0           0           0   0.37433042
## [6,]           0           1           0           0           0  -0.93059797
##      any_smoker smokeSH  mean_cpss  mean_epsd male gest_age_w days_to_peapod
## [1,]          0       1  3.3968005 -1.3157360    0  0.8044835     -0.2392302
## [2,]          0       0  0.1208193 -0.6918928    1 -2.7388783      0.1867962
## [3,]          0       0  0.1208193 -1.0038144    0  0.6971089      0.1867962
## [4,]          0       0  0.4484174 -1.3157360    0 -2.4167545     -0.2392302
## [5,]          0       0 -1.1895732 -1.3157360    1 -0.8061355      0.1867962
## [6,]          0       0 -0.5343769 -1.0038144    0  0.9118581     -0.2392302
summary(W.scaled)
##       lat                lon           lat_lon_int          latina_re     
##  Min.   :-2.46715   Min.   :-2.4830   Min.   :-3.510301   Min.   :0.0000  
##  1st Qu.:-0.62450   1st Qu.:-0.5811   1st Qu.:-0.493286   1st Qu.:0.0000  
##  Median : 0.05945   Median : 0.1064   Median : 0.008488   Median :0.0000  
##  Mean   : 0.00000   Mean   : 0.0000   Mean   : 0.000000   Mean   :0.2628  
##  3rd Qu.: 0.43089   3rd Qu.: 0.6643   3rd Qu.: 0.599123   3rd Qu.:1.0000  
##  Max.   : 4.01365   Max.   : 4.5155   Max.   : 2.628224   Max.   :1.0000  
##     black_re         other_re          ed_no_hs          ed_hs       
##  Min.   :0.0000   Min.   :0.00000   Min.   :0.0000   Min.   :0.0000  
##  1st Qu.:0.0000   1st Qu.:0.00000   1st Qu.:0.0000   1st Qu.:0.0000  
##  Median :0.0000   Median :0.00000   Median :0.0000   Median :0.0000  
##  Mean   :0.1654   Mean   :0.06667   Mean   :0.1538   Mean   :0.1833  
##  3rd Qu.:0.0000   3rd Qu.:0.00000   3rd Qu.:0.0000   3rd Qu.:0.0000  
##  Max.   :1.0000   Max.   :1.00000   Max.   :1.0000   Max.   :1.0000  
##      ed_aa            ed_4yr          low_bmi           ovwt_bmi     
##  Min.   :0.0000   Min.   :0.0000   Min.   :0.00000   Min.   :0.0000  
##  1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.00000   1st Qu.:0.0000  
##  Median :0.0000   Median :0.0000   Median :0.00000   Median :0.0000  
##  Mean   :0.2256   Mean   :0.2205   Mean   :0.03077   Mean   :0.2615  
##  3rd Qu.:0.0000   3rd Qu.:0.0000   3rd Qu.:0.00000   3rd Qu.:1.0000  
##  Max.   :1.0000   Max.   :1.0000   Max.   :1.00000   Max.   :1.0000  
##    obese_bmi      concep_spring    concep_summer   concep_fall    
##  Min.   :0.0000   Min.   :0.0000   Min.   :0.00   Min.   :0.0000  
##  1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.00   1st Qu.:0.0000  
##  Median :0.0000   Median :0.0000   Median :0.00   Median :0.0000  
##  Mean   :0.1962   Mean   :0.2436   Mean   :0.25   Mean   :0.2667  
##  3rd Qu.:0.0000   3rd Qu.:0.0000   3rd Qu.:0.25   3rd Qu.:1.0000  
##  Max.   :1.0000   Max.   :1.0000   Max.   :1.00   Max.   :1.0000  
##   concep_2010      concep_2011      concep_2012      concep_2013    
##  Min.   :0.0000   Min.   :0.0000   Min.   :0.0000   Min.   :0.0000  
##  1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.0000  
##  Median :0.0000   Median :0.0000   Median :0.0000   Median :0.0000  
##  Mean   :0.1692   Mean   :0.2936   Mean   :0.2808   Mean   :0.2551  
##  3rd Qu.:0.0000   3rd Qu.:1.0000   3rd Qu.:1.0000   3rd Qu.:1.0000  
##  Max.   :1.0000   Max.   :1.0000   Max.   :1.0000   Max.   :1.0000  
##   maternal_age       any_smoker         smokeSH         mean_cpss       
##  Min.   :-1.9093   Min.   :0.00000   Min.   :0.0000   Min.   :-6.10355  
##  1st Qu.:-0.9306   1st Qu.:0.00000   1st Qu.:0.0000   1st Qu.:-0.53438  
##  Median : 0.0481   Median :0.00000   Median :0.0000   Median : 0.01162  
##  Mean   : 0.0000   Mean   :0.08718   Mean   :0.2474   Mean   : 0.00000  
##  3rd Qu.: 0.7006   3rd Qu.:0.00000   3rd Qu.:0.0000   3rd Qu.: 0.55762  
##  Max.   : 2.6580   Max.   :1.00000   Max.   :1.0000   Max.   : 3.39680  
##    mean_epsd            male          gest_age_w       days_to_peapod   
##  Min.   :-1.3157   Min.   :0.0000   Min.   :-5.20849   Min.   :-0.6653  
##  1st Qu.:-0.7959   1st Qu.:0.0000   1st Qu.:-0.48401   1st Qu.:-0.2392  
##  Median :-0.1720   Median :1.0000   Median : 0.05286   Median :-0.2392  
##  Mean   : 0.0000   Mean   :0.5064   Mean   : 0.00000   Mean   : 0.0000  
##  3rd Qu.: 0.5558   3rd Qu.:1.0000   3rd Qu.: 0.69711   3rd Qu.:-0.2392  
##  Max.   : 3.9869   Max.   :1.0000   Max.   : 3.81097   Max.   :10.4114

Variance and histograms for the scaled covariates

var(W.scaled)
##                          lat           lon  lat_lon_int      latina_re
## lat             1.0000000000 -0.2294265015 -0.922594810  0.01488040464
## lon            -0.2294265015  1.0000000000  0.587147326  0.00774099102
## lat_lon_int    -0.9225948101  0.5871473257  1.000000000 -0.00928638293
## latina_re       0.0148804046  0.0077409910 -0.009286383  0.19399460189
## black_re       -0.0076765642  0.0416993781  0.022926625 -0.04352226721
## other_re        0.0022244292 -0.0045513219 -0.003662305 -0.01754385965
## ed_no_hs       -0.0002536098  0.0211421973  0.008600587  0.03781968994
## ed_hs          -0.0092915161  0.0376437998  0.022660243  0.03262729996
## ed_aa          -0.0072973858  0.0461167337  0.024355069  0.01250781739
## ed_4yr          0.0084748321 -0.0053108878 -0.009175293 -0.03620683980
## low_bmi        -0.0031399188  0.0031935883  0.003878110 -0.00167868075
## ovwt_bmi        0.0176550362  0.0102854255 -0.010619251  0.02488397354
## obese_bmi       0.0151602612  0.0074254851 -0.009652703  0.02283499556
## concep_spring   0.0203171932 -0.0022492530 -0.017790516 -0.00633619697
## concep_summer  -0.0229599220 -0.0001995618  0.019015261 -0.00417201540
## concep_fall     0.0095582094  0.0161897319 -0.001540859  0.01583226359
## concep_2010     0.0109529805  0.0028301792 -0.008007944 -0.00859089563
## concep_2011    -0.0226544797  0.0224924333  0.027745587 -0.01050821237
## concep_2012     0.0015394008 -0.0023870971 -0.002215499  0.01340475955
## concep_2013     0.0089319968 -0.0236248234 -0.016772917  0.00474803331
## maternal_age    0.0348578763 -0.1930103076 -0.105532928 -0.11130236864
## any_smoker     -0.0069992076  0.0222429459  0.014635045 -0.00753760574
## smokeSH         0.0011347413  0.0442610839  0.016595995 -0.00349725157
## mean_cpss      -0.0279187887 -0.0046586574  0.021381618 -0.04032749691
## mean_epsd      -0.0458873302  0.0573784314  0.060923471  0.03908431534
## male            0.0224103855 -0.0245595335 -0.028364840  0.00152233304
## gest_age_w      0.0302744587 -0.0833518477 -0.058256588 -0.00772944439
## days_to_peapod  0.0166177524 -0.0037582676 -0.015297436 -0.00006310256
##                     black_re      other_re      ed_no_hs         ed_hs
## lat            -0.0076765642  0.0022244292 -0.0002536098 -0.0092915161
## lon             0.0416993781 -0.0045513219  0.0211421973  0.0376437998
## lat_lon_int     0.0229266248 -0.0036623054  0.0086005874  0.0226602429
## latina_re      -0.0435222672 -0.0175438596  0.0378196899  0.0326273000
## black_re        0.1382097363 -0.0110397946  0.0143181594  0.0158536585
## other_re       -0.0110397946  0.0623020967 -0.0025673941  0.0031664527
## ed_no_hs        0.0143181594 -0.0025673941  0.1303446233 -0.0282413350
## ed_hs           0.0158536585  0.0031664527 -0.0282413350  0.1499144202
## ed_aa           0.0178335144  0.0041934104 -0.0347585662 -0.0414206247
## ed_4yr         -0.0172607880 -0.0031664527 -0.0339685988 -0.0404792469
## low_bmi         0.0026068925 -0.0007702182 -0.0034561074 -0.0005134788
## ovwt_bmi        0.0003357362 -0.0059050064  0.0046410586 -0.0069319641
## obese_bmi       0.0073121359  0.0023106547  0.0057272638  0.0268934531
## concep_spring  -0.0005431026  0.0055626872 -0.0028636319  0.0014976466
## concep_summer  -0.0067394095  0.0000000000 -0.0038510911 -0.0060975610
## concep_fall    -0.0069319641 -0.0023962345  0.0102695764  0.0062473256
## concep_2010     0.0117705145 -0.0010269576  0.0008887133  0.0074454429
## concep_2011     0.0155672953 -0.0003423192  0.0112570356 -0.0063970903
## concep_2012    -0.0118346993 -0.0007702182 -0.0047398045  0.0062259307
## concep_2013    -0.0152908068  0.0022250749 -0.0072084527 -0.0070389388
## maternal_age   -0.0914960717 -0.0135406562 -0.1473311448 -0.1061266380
## any_smoker      0.0150883776 -0.0006846384  0.0173792831  0.0045357296
## smokeSH         0.0321961094  0.0065896448  0.0324874099  0.0251818571
## mean_cpss      -0.0362044396  0.0225734779 -0.0574356146 -0.0356451617
## mean_epsd       0.0160927464  0.0210839610  0.0715352956  0.0221439428
## male           -0.0055544584  0.0021394951 -0.0151081268  0.0007488233
## gest_age_w     -0.0459673981 -0.0051550835 -0.0121190054 -0.0148312028
## days_to_peapod  0.0353079864  0.0037188443  0.0068992133  0.0014765999
##                       ed_aa        ed_4yr       low_bmi      ovwt_bmi
## lat            -0.007297386  0.0084748321 -0.0031399188  0.0176550362
## lon             0.046116734 -0.0053108878  0.0031935883  0.0102854255
## lat_lon_int     0.024355069 -0.0091752931  0.0038781104 -0.0106192507
## latina_re       0.012507817 -0.0362068398 -0.0016786808  0.0248839735
## black_re        0.017833514 -0.0172607880  0.0026068925  0.0003357362
## other_re        0.004193410 -0.0031664527 -0.0007702182 -0.0059050064
## ed_no_hs       -0.034758566 -0.0339685988 -0.0034561074  0.0046410586
## ed_hs          -0.041420625 -0.0404792469 -0.0005134788 -0.0069319641
## ed_aa           0.174951450 -0.0498206116  0.0046015602  0.0179322603
## ed_4yr         -0.049820612  0.1721075672 -0.0003752345  0.0013034462
## low_bmi         0.004601560 -0.0003752345  0.0298607682 -0.0080576676
## ovwt_bmi        0.017932260  0.0013034462 -0.0080576676  0.1933840229
## obese_bmi       0.012165498 -0.0137849314 -0.0060432507 -0.0513676311
## concep_spring   0.006583062 -0.0062868240 -0.0049372963  0.0068134689
## concep_summer  -0.010269576  0.0089858793  0.0038510911 -0.0051347882
## concep_fall    -0.010183997  0.0014548567  0.0033376123  0.0046213094
## concep_2010     0.002843883  0.0011454528  0.0024883974 -0.0032388664
## concep_2011     0.002988710  0.0057799282  0.0025081465  0.0065567295
## concep_2012    -0.005668016 -0.0067937198 -0.0047990520 -0.0054902735
## concep_2013    -0.001158619  0.0001514104 -0.0001579935  0.0025081465
## maternal_age   -0.034152305  0.1077776102 -0.0091971230  0.0067327450
## any_smoker      0.008544814 -0.0153977815  0.0011652019 -0.0048582996
## smokeSH         0.021118462 -0.0353773740  0.0026463908 -0.0108818011
## mean_cpss       0.029189204  0.0275174804  0.0079977462 -0.0043164323
## mean_epsd       0.016391602 -0.0481925954  0.0107834260  0.0098080614
## male            0.001119121  0.0062868240 -0.0001974919 -0.0029623778
## gest_age_w     -0.025824190  0.0330362179 -0.0033335217 -0.0159296533
## days_to_peapod  0.025249438 -0.0107106080 -0.0073703791 -0.0139751139
##                   obese_bmi concep_spring concep_summer   concep_fall
## lat             0.015160261  0.0203171932 -0.0229599220  0.0095582094
## lon             0.007425485 -0.0022492530 -0.0001995618  0.0161897319
## lat_lon_int    -0.009652703 -0.0177905156  0.0190152613 -0.0015408589
## latina_re       0.022834996 -0.0063361970 -0.0041720154  0.0158322636
## black_re        0.007312136 -0.0005431026 -0.0067394095 -0.0069319641
## other_re        0.002310655  0.0055626872  0.0000000000 -0.0023962345
## ed_no_hs        0.005727264 -0.0028636319 -0.0038510911  0.0102695764
## ed_hs           0.026893453  0.0014976466 -0.0060975610  0.0062473256
## ed_aa           0.012165498  0.0065830618 -0.0102695764 -0.0101839966
## ed_4yr         -0.013784931 -0.0062868240  0.0089858793  0.0014548567
## low_bmi        -0.006043251 -0.0049372963  0.0038510911  0.0033376123
## ovwt_bmi       -0.051367631  0.0068134689 -0.0051347882  0.0046213094
## obese_bmi       0.157879925 -0.0029130048 -0.0054557125 -0.0048780488
## concep_spring  -0.002913005  0.1844903064 -0.0609756098 -0.0650406504
## concep_summer  -0.005455712 -0.0609756098  0.1877406932 -0.0667522465
## concep_fall    -0.004878049 -0.0650406504 -0.0667522465  0.1958065896
## concep_2010    -0.004996544 -0.0233040387  0.0012836970  0.0267008986
## concep_2011     0.002671077  0.0041308713 -0.0003209243 -0.0129225503
## concep_2012     0.009040190 -0.0119976301  0.0016046213  0.0033376123
## concep_2013    -0.006462921  0.0314834930 -0.0022464698 -0.0167736414
## maternal_age   -0.002069755  0.0029368513  0.0128775828 -0.0263135433
## any_smoker      0.003416609 -0.0007241368  0.0012836970 -0.0014548567
## smokeSH         0.011735953 -0.0051512458 -0.0093068036 -0.0005990586
## mean_cpss      -0.017623185  0.0102636126  0.0090765847 -0.0058688239
## mean_epsd       0.021537334 -0.0093232881 -0.0185691459  0.0210706139
## male            0.000666535 -0.0028471742 -0.0073812580 -0.0017115961
## gest_age_w     -0.018839063 -0.0120553886 -0.0012405281  0.0303791551
## days_to_peapod  0.003874497  0.0061840510 -0.0155863326 -0.0080939552
##                  concep_2010   concep_2011   concep_2012   concep_2013
## lat             0.0109529805 -0.0226544797  0.0015394008  0.0089319968
## lon             0.0028301792  0.0224924333 -0.0023870971 -0.0236248234
## lat_lon_int    -0.0080079439  0.0277455872 -0.0022154991 -0.0167729167
## latina_re      -0.0085908956 -0.0105082124  0.0134047596  0.0047480333
## black_re        0.0117705145  0.0155672953 -0.0118346993 -0.0152908068
## other_re       -0.0010269576 -0.0003423192 -0.0007702182  0.0022250749
## ed_no_hs        0.0008887133  0.0112570356 -0.0047398045 -0.0072084527
## ed_hs           0.0074454429 -0.0063970903  0.0062259307 -0.0070389388
## ed_aa           0.0028438827  0.0029887100 -0.0056680162 -0.0011586189
## ed_4yr          0.0011454528  0.0057799282 -0.0067937198  0.0001514104
## low_bmi         0.0024883974  0.0025081465 -0.0047990520 -0.0001579935
## ovwt_bmi       -0.0032388664  0.0065567295 -0.0054902735  0.0025081465
## obese_bmi      -0.0049965439  0.0026710773  0.0090401896 -0.0064629209
## concep_spring  -0.0233040387  0.0041308713 -0.0119976301  0.0314834930
## concep_summer   0.0012836970 -0.0003209243  0.0016046213 -0.0022464698
## concep_fall     0.0267008986 -0.0129225503  0.0033376123 -0.0167736414
## concep_2010     0.1407721931 -0.0497481979 -0.0475757875 -0.0432309667
## concep_2011    -0.0497481979  0.2076610381 -0.0825367829 -0.0749991771
## concep_2012    -0.0475757875 -0.0825367829  0.2021970969 -0.0717241039
## concep_2013    -0.0432309667 -0.0749991771 -0.0717241039  0.1902817550
## maternal_age   -0.0328905868 -0.0432339945  0.0317389331  0.0462084289
## any_smoker      0.0031993680  0.0090319608 -0.0078206774 -0.0042987393
## smokeSH         0.0094203614  0.0145535038 -0.0182136862 -0.0067262434
## mean_cpss       0.0079265785 -0.0141064917 -0.0086484999  0.0104679503
## mean_epsd      -0.0144672243  0.0406582459 -0.0297416911  0.0052396759
## male            0.0014811889 -0.0050936441  0.0014071295  0.0028554030
## gest_age_w     -0.0066182705 -0.0045846526  0.0012150814  0.0089551286
## days_to_peapod -0.0279586414 -0.0014177042 -0.0328007113  0.0624841560
##                maternal_age    any_smoker       smokeSH    mean_cpss
## lat             0.034857876 -0.0069992076  0.0011347413 -0.027918789
## lon            -0.193010308  0.0222429459  0.0442610839 -0.004658657
## lat_lon_int    -0.105532928  0.0146350446  0.0165959949  0.021381618
## latina_re      -0.111302369 -0.0075376057 -0.0034972516 -0.040327497
## black_re       -0.091496072  0.0150883776  0.0321961094 -0.036204440
## other_re       -0.013540656 -0.0006846384  0.0065896448  0.022573478
## ed_no_hs       -0.147331145  0.0173792831  0.0324874099 -0.057435615
## ed_hs          -0.106126638  0.0045357296  0.0251818571 -0.035645162
## ed_aa          -0.034152305  0.0085448142  0.0211184622  0.029189204
## ed_4yr          0.107777610 -0.0153977815 -0.0353773740  0.027517480
## low_bmi        -0.009197123  0.0011652019  0.0026463908  0.007997746
## ovwt_bmi        0.006732745 -0.0048582996 -0.0108818011 -0.004316432
## obese_bmi      -0.002069755  0.0034166091  0.0117359534 -0.017623185
## concep_spring   0.002936851 -0.0007241368 -0.0051512458  0.010263613
## concep_summer   0.012877583  0.0012836970 -0.0093068036  0.009076585
## concep_fall    -0.026313543 -0.0014548567 -0.0005990586 -0.005868824
## concep_2010    -0.032890587  0.0031993680  0.0094203614  0.007926578
## concep_2011    -0.043233995  0.0090319608  0.0145535038 -0.014106492
## concep_2012     0.031738933 -0.0078206774 -0.0182136862 -0.008648500
## concep_2013     0.046208429 -0.0042987393 -0.0067262434  0.010467950
## maternal_age    1.000000000 -0.0452178456 -0.1497337791  0.111663918
## any_smoker     -0.045217846  0.0796813798  0.0490043119  0.012438902
## smokeSH        -0.149733779  0.0490043119  0.1864504131  0.022013301
## mean_cpss       0.111663918  0.0124389018  0.0220133014  1.000000000
## mean_epsd      -0.170707705  0.0453127030  0.1111391210  0.441020650
## male            0.026063884  0.0020078338  0.0016210790 -0.007214721
## gest_age_w      0.073088144 -0.0297069373 -0.0509973685 -0.007275391
## days_to_peapod -0.001591990 -0.0022885196  0.0107316422 -0.005995421
##                   mean_epsd          male   gest_age_w days_to_peapod
## lat            -0.045887330  0.0224103855  0.030274459  0.01661775239
## lon             0.057378431 -0.0245595335 -0.083351848 -0.00375826760
## lat_lon_int     0.060923471 -0.0283648398 -0.058256588 -0.01529743598
## latina_re       0.039084315  0.0015223330 -0.007729444 -0.00006310256
## black_re        0.016092746 -0.0055544584 -0.045967398  0.03530798637
## other_re        0.021083961  0.0021394951 -0.005155083  0.00371884427
## ed_no_hs        0.071535296 -0.0151081268 -0.012119005  0.00689921335
## ed_hs           0.022143943  0.0007488233 -0.014831203  0.00147659993
## ed_aa           0.016391602  0.0011191205 -0.025824190  0.02524943813
## ed_4yr         -0.048192595  0.0062868240  0.033036218 -0.01071060804
## low_bmi         0.010783426 -0.0001974919 -0.003333522 -0.00737037914
## ovwt_bmi        0.009808061 -0.0029623778 -0.015929653 -0.01397511387
## obese_bmi       0.021537334  0.0006665350 -0.018839063  0.00387449725
## concep_spring  -0.009323288 -0.0028471742 -0.012055389  0.00618405099
## concep_summer  -0.018569146 -0.0073812580 -0.001240528 -0.01558633260
## concep_fall     0.021070614 -0.0017115961  0.030379155 -0.00809395517
## concep_2010    -0.014467224  0.0014811889 -0.006618270 -0.02795864142
## concep_2011     0.040658246 -0.0050936441 -0.004584653 -0.00141770421
## concep_2012    -0.029741691  0.0014071295  0.001215081 -0.03280071127
## concep_2013     0.005239676  0.0028554030  0.008955129  0.06248415603
## maternal_age   -0.170707705  0.0260638841  0.073088144 -0.00159199026
## any_smoker      0.045312703  0.0020078338 -0.029706937 -0.00228851955
## smokeSH         0.111139121  0.0016210790 -0.050997369  0.01073164223
## mean_cpss       0.441020650 -0.0072147212 -0.007275391 -0.00599542077
## mean_epsd       1.000000000 -0.0104804641 -0.086750438  0.01124930187
## male           -0.010480464  0.2502797801 -0.039081937  0.03073094727
## gest_age_w     -0.086750438 -0.0390819370  1.000000000 -0.13525838557
## days_to_peapod  0.011249302  0.0307309473 -0.135258386  1.00000000000
ggplot(pivot_longer(as.data.frame(W.scaled), lat:gest_age_w, 
                    names_to = "exp", values_to = "value")) + 
    geom_histogram(aes(x = value)) + 
    facet_wrap(~ exp, scales = "free")
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

1.3 Response data: adiposty (%fat mass)

Y <- select(hs_data2, adiposity) %>%
  as.matrix()
head(Y)
##      adiposity
## [1,]  9.217429
## [2,]  7.736959
## [3,] 13.474442
## [4,] 10.058402
## [5,] 11.836774
## [6,] 15.544041

Distribution of adiposity and scaled adiposity

hist(Y, breaks = 20)

hist(scale(Y), breaks = 20)

1.4 Scatterplots of exposures and outcome (adiposity)

Both adiposity (Y) and the exposures are scaled here

NOTE: Don’t use these plots as a way to estimate how many predictors might make the cut. This should be done a priori

df <- as.data.frame(cbind(scale(Y), X.scaled))
# par(mfrow=c(5,4))
sapply(2:length(df), function(x){
  lm.x <- lm(adiposity ~ df[,x], data = df)
  plot(df[,c(x, 1)],
       xlab = paste0(colnames(df)[x], " beta: ",
                     round(summary(lm.x)$coef[2,1],4),
                     "; p = ",
                     round(summary(lm.x)$coef[2,4],4)))
  abline(lm.x)
})

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2 Is gestational age a potenital mediator?

I.e., is there a relationship between our exposures and gestational age?

The DAG might look something like this:

exposures —> gestational age —> adiposity _________________________________^

2.1 Scatter plots for exposures and gestational age

Both gestational age and the exposures are scaled here. Gestational age measured in weeks from estimated date of conception to delivery

Since there were some (small) relationships between exposures and gestational age (based on simple linear regression models– namely the ozone and SES indicators), I’m going to omit this covariate for now.

df2 <- as.data.frame(cbind(W.scaled[,"gest_age_w"], X.scaled))
colnames(df2)[1] <- "gest_age_w"
# par(mfrow=c(5,4))
sapply(2:length(df2), function(x){
  lm.x <- lm(gest_age_w ~ df2[,x], data = df2)
  plot(df2[,c(x, 1)],
       xlab = paste0(colnames(df2)[x], " beta: ",
                     round(summary(lm.x)$coef[2,1],4),
                     "; p = ",
                     round(summary(lm.x)$coef[2,4],4)))
  abline(lm.x)
})

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Dropping gest_age_w from the covariates

colnames(W.scaled)
##  [1] "lat"            "lon"            "lat_lon_int"    "latina_re"     
##  [5] "black_re"       "other_re"       "ed_no_hs"       "ed_hs"         
##  [9] "ed_aa"          "ed_4yr"         "low_bmi"        "ovwt_bmi"      
## [13] "obese_bmi"      "concep_spring"  "concep_summer"  "concep_fall"   
## [17] "concep_2010"    "concep_2011"    "concep_2012"    "concep_2013"   
## [21] "maternal_age"   "any_smoker"     "smokeSH"        "mean_cpss"     
## [25] "mean_epsd"      "male"           "gest_age_w"     "days_to_peapod"
W.scaled2 <- W.scaled[,-c(ncol(W.scaled)-1)]
colnames(W.scaled2)
##  [1] "lat"            "lon"            "lat_lon_int"    "latina_re"     
##  [5] "black_re"       "other_re"       "ed_no_hs"       "ed_hs"         
##  [9] "ed_aa"          "ed_4yr"         "low_bmi"        "ovwt_bmi"      
## [13] "obese_bmi"      "concep_spring"  "concep_summer"  "concep_fall"   
## [17] "concep_2010"    "concep_2011"    "concep_2012"    "concep_2013"   
## [21] "maternal_age"   "any_smoker"     "smokeSH"        "mean_cpss"     
## [25] "mean_epsd"      "male"           "days_to_peapod"

3 RIDGE regression

To see if there might be something going on, Lauren suggested a ridge regression with a small penalty.

set.seed(123)

library(glmnet)
## Loading required package: Matrix
## 
## Attaching package: 'Matrix'
## The following objects are masked from 'package:tidyr':
## 
##     expand, pack, unpack
## Loaded glmnet 4.0-2
lambda_seq <- 10^seq(4, -4, by = -.05)

#' Best lambda from CV
ridge_cv <- cv.glmnet(X, Y, alpha = 0, lambda = lambda_seq,
                      standardize = T, standardize.response = T)
plot(ridge_cv)

best_lambda <- ridge_cv$lambda.min
best_lambda
## [1] 31.62278
#' Fit the model using the best_lambda
ad_ridge <- glmnet(X, Y, alpha = 0, lambda = best_lambda,
                   standardize = T, standardize.response = T)
summary(ad_ridge)
##           Length Class     Mode   
## a0         1     -none-    numeric
## beta      21     dgCMatrix S4     
## df         1     -none-    numeric
## dim        2     -none-    numeric
## lambda     1     -none-    numeric
## dev.ratio  1     -none-    numeric
## nulldev    1     -none-    numeric
## npasses    1     -none-    numeric
## jerr       1     -none-    numeric
## offset     1     -none-    logical
## call       7     -none-    call   
## nobs       1     -none-    numeric

Ridge regression coefficients

coef(ad_ridge)
## 22 x 1 sparse Matrix of class "dgCMatrix"
##                                    s0
## (Intercept)          9.62868020454909
## mean_pm             -0.02639965648569
## mean_o3             -0.00149863384507
## mean_temp            0.00035436690634
## pct_tree_cover      -0.00639632089744
## pct_impervious      -0.00115374895744
## mean_aadt_intensity  0.00000005413306
## dist_m_tri           0.00000254982195
## dist_m_npl           0.00000201927869
## dist_m_waste_site    0.00001122409928
## dist_m_major_emit    0.00000316525795
## dist_m_cafo         -0.00000138036863
## dist_m_mine_well    -0.00000693864929
## cvd_rate_adj        -0.00037383477626
## res_rate_adj        -0.00077204501915
## violent_crime_rate  -0.00212155361425
## property_crime_rate -0.00074961143159
## pct_less_hs         -0.00020615684880
## pct_unemp           -0.00414540443803
## pct_limited_eng      0.00144754271022
## pct_hh_pov          -0.00182634711100
## pct_poc              0.00029616109913

Ridge regression predictions

ridge_pred <- predict(ad_ridge, newx = X)
plot(Y, ridge_pred)

actual <- Y
preds <- ridge_pred
rsq <- 1 - (sum((preds - actual) ^ 2))/(sum((actual - mean(actual)) ^ 2))

The R2 value for this model is 0.01. Based on these results, it doesn’t look like there’s much here.

4 Nonparametric Bayesian Shrinkage (NPB): Adiposity

Still, we wanted to try to fit the NPB model with these data.

4.1 Finding the NPB priors

I’m starting with the sets of priors used in the birth weight analysis. Note: I’m including far fewer iterations of the priors than in the previous version of the document.

4.1.1 Vignette Priors

set.seed(123)

priors.npb.1 <- list(alpha.pi = 1, beta.pi = 1, alpha.pi2 = 9, beta.pi2 = 1,
                     a.phi1 = 1)

fit.npb.1 <- npb(niter = 1000, nburn = 500, X = X.scaled, Y = Y, W = W.scaled2,
                 scaleY = TRUE,
                 priors = priors.npb.1, interact = F)
npb.sum.1 <- summary(fit.npb.1)
npb.sum.1$main.effects
##       Posterior Mean         SD 95% CI Lower 95% CI Upper   PIP
##  [1,] -0.00251899160 0.01678945  -0.03975440    0.0000000 0.060
##  [2,] -0.00697160371 0.03431486  -0.09811891    0.0000000 0.092
##  [3,] -0.00380585290 0.02717848  -0.05020675    0.0000000 0.074
##  [4,] -0.00003156695 0.02579996  -0.02895671    0.0000000 0.060
##  [5,] -0.00334740285 0.02130686  -0.04523678    0.0000000 0.072
##  [6,]  0.00014552465 0.02280629  -0.02096066    0.0000000 0.050
##  [7,] -0.00348068643 0.02742249  -0.05043653    0.0000000 0.068
##  [8,] -0.00223689808 0.01510690  -0.03758662    0.0000000 0.062
##  [9,]  0.00972022234 0.06317830  -0.01193044    0.1676507 0.070
## [10,] -0.00184770555 0.01893606  -0.04149589    0.0000000 0.072
## [11,] -0.00177345723 0.04496029  -0.04607937    0.0000000 0.086
## [12,] -0.00385506190 0.01966658  -0.06590866    0.0000000 0.072
## [13,] -0.00418350090 0.02432050  -0.05298671    0.0000000 0.072
## [14,] -0.00478567731 0.02835075  -0.08053355    0.0000000 0.082
## [15,] -0.00563577569 0.02816203  -0.08053355    0.0000000 0.078
## [16,] -0.00886650240 0.04640896  -0.11897728    0.0000000 0.096
## [17,] -0.00339000993 0.02288352  -0.03975440    0.0000000 0.060
## [18,] -0.00500625385 0.03089999  -0.06444760    0.0000000 0.078
## [19,] -0.00301121979 0.02423689  -0.04945271    0.0000000 0.070
## [20,] -0.00451592686 0.02868031  -0.05662754    0.0000000 0.064
## [21,] -0.00139528546 0.01676618  -0.02895671    0.0000000 0.050
plot(fit.npb.1$beta[,1], type = "l")

plot(fit.npb.1$beta[,2], type = "l")

plot(fit.npb.1$beta[,13], type = "l")

4.1.2 Adjust alpha.pi and beta.pi

For now, leave a.phi1 and sig2inv.mu1 alone for now.

alpha.pi and beta.pi are responisble for the exclusion probability distribution. If we thing we want ~50% of our covariates, we need the mass of this distribution to be somewhere between 0.4 and 0.6. To do this, we set alpha.pi and beta.pi to the same value

4.1.2.1 Try making alpha.pi and beta.pi 2

plot(density(rbeta(10000, 2, 2)))

priors.npb.12 <- list(alpha.pi = 2, beta.pi = 2, alpha.pi2 = 9, beta.pi2 = 1,
                     a.phi1 = 1, sig2inv.mu1 = 1)

fit.npb.12 <- npb(niter = 1000, nburn = 500, X = X.scaled, Y = Y, W = W.scaled2,
                 scaleY = TRUE,
                 priors = priors.npb.12, interact = F)
npb.sum.12 <- summary(fit.npb.12)
npb.sum.12$main.effects
##       Posterior Mean         SD 95% CI Lower 95% CI Upper   PIP
##  [1,]  -0.0059157857 0.03377064 -0.097474005 0.0004792181 0.100
##  [2,]  -0.0090463153 0.04653504 -0.125840618 0.0000000000 0.096
##  [3,]  -0.0084161455 0.05013707 -0.093931093 0.0000000000 0.106
##  [4,]  -0.0010198837 0.02505189 -0.054480140 0.0217012935 0.104
##  [5,]  -0.0048418847 0.02761684 -0.078374498 0.0000000000 0.114
##  [6,]   0.0036931673 0.03794773 -0.025612089 0.0392846127 0.094
##  [7,]  -0.0042454533 0.02797184 -0.072847918 0.0051278635 0.104
##  [8,]  -0.0017935003 0.02515603 -0.065048094 0.0190562753 0.106
##  [9,]   0.0149951440 0.07430073 -0.003587089 0.2867707922 0.106
## [10,]  -0.0009999632 0.02067231 -0.049277540 0.0004792181 0.090
## [11,]  -0.0101864863 0.09483126 -0.145606427 0.0000000000 0.126
## [12,]  -0.0114217248 0.06188157 -0.199081888 0.0000000000 0.136
## [13,]  -0.0090265096 0.04872197 -0.132097009 0.0000000000 0.118
## [14,]  -0.0061123210 0.03001042 -0.086376809 0.0000000000 0.108
## [15,]  -0.0040302357 0.02241392 -0.065048094 0.0000000000 0.094
## [16,]  -0.0276631513 0.08308158 -0.340079717 0.0000000000 0.186
## [17,]  -0.0076031044 0.04357811 -0.095937097 0.0000000000 0.104
## [18,]  -0.0150402911 0.05389089 -0.216817306 0.0000000000 0.132
## [19,]  -0.0025016035 0.02953072 -0.064428284 0.0000000000 0.104
## [20,]  -0.0082003857 0.04223308 -0.107988449 0.0000000000 0.108
## [21,]  -0.0047967090 0.03196737 -0.065560690 0.0000000000 0.110
plot(fit.npb.12$beta[,1], type = "l")

plot(fit.npb.12$beta[,2], type = "l")

plot(fit.npb.12$beta[,13], type = "l")

4.1.2.2 Try making alpha.pi and beta.pi 5

plot(density(rbeta(10000, 5, 5)))

priors.npb.13 <- list(alpha.pi = 5, beta.pi = 5, alpha.pi2 = 9, beta.pi2 = 1,
                     a.phi1 = 1, sig2inv.mu1 = 1)

fit.npb.13 <- npb(niter = 1000, nburn = 500, X = X.scaled, Y = Y, W = W.scaled2,
                 scaleY = TRUE,
                 priors = priors.npb.13, interact = F)
npb.sum.13 <- summary(fit.npb.13)
npb.sum.13$main.effects
##       Posterior Mean         SD 95% CI Lower 95% CI Upper   PIP
##  [1,]   -0.013588720 0.04611916  -0.15037954  0.037021341 0.268
##  [2,]   -0.022858449 0.06363567  -0.19568711  0.030966082 0.328
##  [3,]   -0.022398483 0.05952143  -0.19333262  0.023371966 0.300
##  [4,]   -0.012316437 0.04241531  -0.13775235  0.054945953 0.294
##  [5,]   -0.013926848 0.04523430  -0.15122532  0.027201280 0.260
##  [6,]    0.001723776 0.04522218  -0.07693582  0.117673348 0.210
##  [7,]   -0.017005195 0.05234701  -0.15205642  0.070711829 0.318
##  [8,]   -0.006933887 0.04615876  -0.13601461  0.080466077 0.220
##  [9,]    0.009446499 0.06808085  -0.07788313  0.197738383 0.244
## [10,]   -0.002334525 0.04383212  -0.09189281  0.096615301 0.196
## [11,]   -0.020998685 0.07842284  -0.19413381  0.082415616 0.306
## [12,]   -0.029195737 0.06329614  -0.20285059  0.027583540 0.376
## [13,]   -0.024036571 0.06086846  -0.19859113  0.016850333 0.328
## [14,]   -0.031272317 0.06841559  -0.22156602  0.022314462 0.358
## [15,]   -0.018240412 0.04725588  -0.14530987  0.019420516 0.306
## [16,]   -0.051474739 0.09408527  -0.35645755  0.010528957 0.442
## [17,]   -0.018036891 0.05530325  -0.16237043  0.033679902 0.298
## [18,]   -0.032465349 0.07385592  -0.23134535  0.007372234 0.338
## [19,]   -0.008807566 0.04766809  -0.12392119  0.064478826 0.246
## [20,]   -0.023856852 0.05857587  -0.17456581  0.017484307 0.334
## [21,]   -0.011081707 0.04484714  -0.13407593  0.044814024 0.250
plot(fit.npb.13$beta[,1], type = "l")

plot(fit.npb.13$beta[,2], type = "l")

plot(fit.npb.13$beta[,13], type = "l")

4.1.2.3 Try making alpha.pi and beta.pi 8

plot(density(rbeta(10000, 8, 8)))

priors.npb.14 <- list(alpha.pi = 8, beta.pi = 8, alpha.pi2 = 9, beta.pi2 = 1,
                     a.phi1 = 1, sig2inv.mu1 = 1)

fit.npb.14 <- npb(niter = 1000, nburn = 500, X = X.scaled, Y = Y, W = W.scaled2,
                 scaleY = TRUE,
                 priors = priors.npb.14, interact = F)
npb.sum.14 <- summary(fit.npb.14)
npb.sum.14$main.effects
##       Posterior Mean         SD 95% CI Lower 95% CI Upper   PIP
##  [1,]   -0.022061537 0.05066124  -0.16903610  0.021328953 0.354
##  [2,]   -0.035572741 0.08072661  -0.21655345  0.001175437 0.392
##  [3,]   -0.029063308 0.06705238  -0.18522465  0.025599131 0.410
##  [4,]   -0.016688688 0.04520342  -0.12922315  0.019569688 0.288
##  [5,]   -0.019509063 0.04647884  -0.13604458  0.011084979 0.340
##  [6,]   -0.005721694 0.03198458  -0.08768640  0.050736780 0.230
##  [7,]   -0.020214668 0.04548239  -0.15356206  0.009911258 0.322
##  [8,]   -0.010806016 0.03964471  -0.11704121  0.029248016 0.250
##  [9,]    0.004633821 0.06718315  -0.09404629  0.204561960 0.250
## [10,]   -0.009604285 0.03273550  -0.09972599  0.020629427 0.244
## [11,]   -0.030995485 0.10296062  -0.24465104  0.028408061 0.348
## [12,]   -0.036142851 0.07133508  -0.21246289  0.008649130 0.414
## [13,]   -0.025958870 0.05273096  -0.15434401  0.018678411 0.378
## [14,]   -0.031207791 0.05852112  -0.17103657  0.000000000 0.398
## [15,]   -0.024205608 0.04438088  -0.12917096  0.000000000 0.372
## [16,]   -0.061300783 0.09471326  -0.35912763  0.009911258 0.572
## [17,]   -0.029055401 0.06341583  -0.19199711  0.000000000 0.360
## [18,]   -0.044276687 0.08323885  -0.28271902  0.000000000 0.466
## [19,]   -0.010766467 0.04328633  -0.10957762  0.012961829 0.258
## [20,]   -0.028833342 0.06552176  -0.16440310  0.032408014 0.426
## [21,]   -0.014307547 0.05244701  -0.13145177  0.032408014 0.332
plot(fit.npb.14$beta[,1], type = "l")

plot(fit.npb.14$beta[,2], type = "l")

plot(fit.npb.14$beta[,13], type = "l")

4.1.3 Set alpha.pi and beta.pi to 5, readjust a.phi1 and sig2inv.mu1

Set alpha.pi and beta.pi to 5, rather than 8, and try adjusting a.phi1 and sig2inv.mu1

4.1.3.1 Try making a.phi1 = 10 and sig2inv.mu1 = 1

priors.npb.23 <- list(alpha.pi = 5, beta.pi = 5, alpha.pi2 = 9, beta.pi2 = 1,
                     a.phi1 = 10, sig2inv.mu1 = 1)

fit.npb.23 <- npb(niter = 1000, nburn = 500, X = X.scaled, Y = Y, W = W.scaled2,
                 scaleY = TRUE,
                 priors = priors.npb.23, interact = F)
npb.sum.23 <- summary(fit.npb.23)
npb.sum.23$main.effects
##       Posterior Mean         SD 95% CI Lower 95% CI Upper   PIP
##  [1,]   -0.019660880 0.05820927  -0.18105250  0.039970408 0.350
##  [2,]   -0.034407622 0.09020064  -0.24975240  0.027123403 0.358
##  [3,]   -0.023314205 0.08961590  -0.25125519  0.091702461 0.396
##  [4,]   -0.012069578 0.05024636  -0.13865664  0.068535705 0.298
##  [5,]   -0.016719850 0.04900707  -0.15113382  0.025023931 0.280
##  [6,]    0.002090062 0.05927988  -0.09240788  0.144546324 0.226
##  [7,]   -0.016457220 0.05481142  -0.18551703  0.038588662 0.306
##  [8,]   -0.006310993 0.04581469  -0.11327386  0.087599079 0.282
##  [9,]    0.020952898 0.09391984  -0.07714869  0.327656953 0.282
## [10,]   -0.007427259 0.04372896  -0.10892163  0.085280776 0.262
## [11,]   -0.028601270 0.09160631  -0.26113461  0.030443581 0.360
## [12,]   -0.034856015 0.07817430  -0.25546804  0.045323348 0.418
## [13,]   -0.029578632 0.06584658  -0.21727638  0.020161206 0.360
## [14,]   -0.025649481 0.06680583  -0.21735549  0.043724461 0.362
## [15,]   -0.015104051 0.05374696  -0.13996600  0.030443581 0.312
## [16,]   -0.061796873 0.10230128  -0.34207021  0.007733966 0.494
## [17,]   -0.024187697 0.06552762  -0.22722487  0.020151935 0.320
## [18,]   -0.046991631 0.08782292  -0.31120390  0.017471708 0.436
## [19,]   -0.001825107 0.06816709  -0.11245993  0.159510801 0.288
## [20,]   -0.029272034 0.06400930  -0.21848942  0.029427512 0.392
## [21,]   -0.010968743 0.04828661  -0.12980503  0.043451807 0.262
plot(fit.npb.23$beta[,1], type = "l")

plot(fit.npb.23$beta[,2], type = "l")

plot(fit.npb.23$beta[,13], type = "l")

4.1.3.2 Try making a.phi1 = 10 and sig2inv.mu1 = 10

priors.npb.24 <- list(alpha.pi = 5, beta.pi = 5, alpha.pi2 = 9, beta.pi2 = 1,
                     a.phi1 = 10, sig2inv.mu1 = 10)

fit.npb.24 <- npb(niter = 1000, nburn = 500, X = X.scaled, Y = Y, W = W.scaled2,
                 scaleY = TRUE,
                 priors = priors.npb.24, interact = F)
npb.sum.24 <- summary(fit.npb.24)
npb.sum.24$main.effects
##       Posterior Mean         SD 95% CI Lower 95% CI Upper   PIP
##  [1,]   -0.015441228 0.05365709  -0.18778448  0.053517848 0.288
##  [2,]   -0.028470447 0.08446267  -0.28886105  0.079914717 0.338
##  [3,]   -0.025337886 0.07808192  -0.20855982  0.094913039 0.362
##  [4,]   -0.009717591 0.04672317  -0.13688508  0.055852529 0.236
##  [5,]   -0.014361906 0.05980997  -0.16417365  0.070136787 0.284
##  [6,]    0.006949586 0.05723496  -0.08069088  0.201369407 0.226
##  [7,]   -0.010557068 0.05331814  -0.14436623  0.094815375 0.294
##  [8,]   -0.006925859 0.05136525  -0.14295520  0.071612126 0.248
##  [9,]    0.024503264 0.09474062  -0.07387488  0.320912825 0.258
## [10,]   -0.001739784 0.04960022  -0.11195806  0.106455398 0.216
## [11,]   -0.021143388 0.15092839  -0.29339219  0.150093071 0.382
## [12,]   -0.036434479 0.08671000  -0.25716559  0.049885098 0.380
## [13,]   -0.029240323 0.07398375  -0.25917362  0.027746224 0.344
## [14,]   -0.031740847 0.07309448  -0.23224002  0.038268538 0.346
## [15,]   -0.014061195 0.05869838  -0.16291040  0.111520930 0.304
## [16,]   -0.080689978 0.11661307  -0.41096455  0.013294434 0.554
## [17,]   -0.022079512 0.06342719  -0.19668896  0.043196527 0.312
## [18,]   -0.053901519 0.10356736  -0.36311726  0.007025148 0.420
## [19,]   -0.003006123 0.06095941  -0.11953655  0.076946265 0.248
## [20,]   -0.033875702 0.09073772  -0.28665517  0.037627795 0.346
## [21,]   -0.004821275 0.05669930  -0.13310703  0.118293021 0.280
plot(fit.npb.24$beta[,1], type = "l")

plot(fit.npb.24$beta[,2], type = "l")

plot(fit.npb.24$beta[,13], type = "l")

plot(fit.npb.24$beta[,15], type = "l")

4.2 Fit the NPB model without temperature

As with the birth weight model, I’ve used the 24th set of priors and set scaleY = T in the NPB model below

The priors are as follows: r priors.npb.24

Note that this version of the model does not include gest_age_w. It does include an indicator variable for season of conception (ref = winter) and the lon/lat as covariates and the percentage of the census tract population that is not NHW as an exposure

priors.npb <- priors.npb.24

#' Exposures
colnames(X.scaled)
##  [1] "mean_pm"             "mean_o3"             "mean_temp"          
##  [4] "pct_tree_cover"      "pct_impervious"      "mean_aadt_intensity"
##  [7] "dist_m_tri"          "dist_m_npl"          "dist_m_waste_site"  
## [10] "dist_m_major_emit"   "dist_m_cafo"         "dist_m_mine_well"   
## [13] "cvd_rate_adj"        "res_rate_adj"        "violent_crime_rate" 
## [16] "property_crime_rate" "pct_less_hs"         "pct_unemp"          
## [19] "pct_limited_eng"     "pct_hh_pov"          "pct_poc"
#' Covariates
colnames(W.scaled2)
##  [1] "lat"            "lon"            "lat_lon_int"    "latina_re"     
##  [5] "black_re"       "other_re"       "ed_no_hs"       "ed_hs"         
##  [9] "ed_aa"          "ed_4yr"         "low_bmi"        "ovwt_bmi"      
## [13] "obese_bmi"      "concep_spring"  "concep_summer"  "concep_fall"   
## [17] "concep_2010"    "concep_2011"    "concep_2012"    "concep_2013"   
## [21] "maternal_age"   "any_smoker"     "smokeSH"        "mean_cpss"     
## [25] "mean_epsd"      "male"           "days_to_peapod"
# fit.npb <- npb(niter = 5000, nburn = 2500, X = X.scaled[,-c(3)], Y = Y, W = W.scaled2,
#                scaleY = TRUE,
#                priors = priors.npb, interact = TRUE, XWinteract = TRUE)
# save(fit.npb, file = here::here("Results", "NPB_Adiposity_v4.1.rdata"))

load(here::here("Results", "NPB_Adiposity_v4.1.rdata"))
npb.sum <- summary(fit.npb)

4.2.1 First, main effect regression coefficients with PIPs

rownames(npb.sum$main.effects) <- colnames(X.scaled[,-c(3)])
npb.sum$main.effects
##                     Posterior Mean         SD 95% CI Lower 95% CI Upper    PIP
## mean_pm               -0.010474845 0.05806874  -0.16399269   0.09724534 0.2764
## mean_o3               -0.033949010 0.09432840  -0.28579075   0.07311140 0.3588
## pct_tree_cover        -0.009346531 0.05886109  -0.16062807   0.09357882 0.2632
## pct_impervious        -0.014880529 0.05962135  -0.18533079   0.07258529 0.2744
## mean_aadt_intensity    0.011290602 0.06682281  -0.08592180   0.22515423 0.2484
## dist_m_tri            -0.011534156 0.05975592  -0.17693313   0.10495805 0.2920
## dist_m_npl            -0.002432396 0.05385284  -0.11687455   0.12756605 0.2504
## dist_m_waste_site      0.036118100 0.11404884  -0.07255974   0.41154804 0.3076
## dist_m_major_emit      0.003220441 0.06080674  -0.10592586   0.16131841 0.2420
## dist_m_cafo           -0.018319667 0.11981956  -0.25346625   0.14292422 0.3296
## dist_m_mine_well      -0.031663404 0.08083920  -0.26217059   0.06582362 0.3644
## cvd_rate_adj          -0.025554316 0.06995234  -0.22843583   0.04040998 0.3272
## res_rate_adj          -0.028767538 0.07078109  -0.24269889   0.02615036 0.3240
## violent_crime_rate    -0.013232550 0.05730721  -0.16241997   0.07338247 0.2828
## property_crime_rate   -0.072316252 0.12054928  -0.41474130   0.01445510 0.4804
## pct_less_hs           -0.023573510 0.07524972  -0.24386951   0.06150607 0.3172
## pct_unemp             -0.041639684 0.09036861  -0.31903345   0.02255897 0.3688
## pct_limited_eng        0.004783383 0.07139322  -0.10506007   0.21378057 0.2556
## pct_hh_pov            -0.026256590 0.07209033  -0.23969670   0.02728443 0.3060
## pct_poc               -0.004844897 0.06327005  -0.14293627   0.13767274 0.2588

4.2.3 Interactions

Next, all of the interactions between exposures or between exposures and covariates

npb.sum$interactions
##          Posterior Mean           SD 95% CI Lower 95% CI Upper    PIP
##   [1,]  0.0000751661711 0.0097209821            0            0 0.0020
##   [2,] -0.0002005788630 0.0053181183            0            0 0.0020
##   [3,] -0.0009736546023 0.0148194729            0            0 0.0056
##   [4,] -0.0001366858739 0.0046123749            0            0 0.0020
##   [5,] -0.0003487244809 0.0068381440            0            0 0.0028
##   [6,] -0.0003818031305 0.0105623761            0            0 0.0024
##   [7,] -0.0016712854795 0.0174415421            0            0 0.0112
##   [8,] -0.0016522754155 0.0188527818            0            0 0.0100
##   [9,] -0.0004154454531 0.0076703535            0            0 0.0040
##  [10,] -0.0004777693515 0.0097924987            0            0 0.0032
##  [11,] -0.0004619597843 0.0084150880            0            0 0.0032
##  [12,] -0.0000893656268 0.0047993951            0            0 0.0024
##  [13,] -0.0002095716927 0.0058911499            0            0 0.0024
##  [14,] -0.0001837452631 0.0056096089            0            0 0.0024
##  [15,] -0.0007198374311 0.0115484137            0            0 0.0044
##  [16,] -0.0006202284124 0.0109699259            0            0 0.0040
##  [17,] -0.0016713461178 0.0190179294            0            0 0.0092
##  [18,] -0.0000556291708 0.0031681937            0            0 0.0016
##  [19,] -0.0011153657671 0.0139346470            0            0 0.0076
##  [20,] -0.0000277882137 0.0025423615            0            0 0.0020
##  [21,]  0.0000050283688 0.0050812918            0            0 0.0012
##  [22,] -0.0000205910561 0.0021767022            0            0 0.0016
##  [23,] -0.0004864193355 0.0092428335            0            0 0.0048
##  [24,] -0.0002280010578 0.0051817655            0            0 0.0020
##  [25,] -0.0005492529542 0.0092032004            0            0 0.0048
##  [26,] -0.0000428632044 0.0021431602            0            0 0.0004
##  [27,] -0.0007758221035 0.0133243551            0            0 0.0048
##  [28,] -0.0005808888965 0.0093148563            0            0 0.0048
##  [29,]  0.0000935828564 0.0030264004            0            0 0.0020
##  [30,]  0.0000216538378 0.0024962398            0            0 0.0020
##  [31,]  0.0000205819623 0.0045398891            0            0 0.0016
##  [32,]  0.0001612371806 0.0058900825            0            0 0.0020
##  [33,] -0.0005744216191 0.0100806044            0            0 0.0036
##  [34,] -0.0002234808194 0.0047085284            0            0 0.0036
##  [35,] -0.0001105074658 0.0035494088            0            0 0.0012
##  [36,] -0.0000676933179 0.0029969467            0            0 0.0016
##  [37,] -0.0006507474995 0.0101481756            0            0 0.0048
##  [38,]  0.0000000000000 0.0000000000            0            0 0.0000
##  [39,]  0.0000941503249 0.0070910638            0            0 0.0016
##  [40,] -0.0000298125854 0.0025779712            0            0 0.0020
##  [41,] -0.0003359374637 0.0078172823            0            0 0.0024
##  [42,] -0.0000808032198 0.0029041695            0            0 0.0008
##  [43,]  0.0000861814881 0.0063388937            0            0 0.0024
##  [44,] -0.0002636773428 0.0073892538            0            0 0.0020
##  [45,] -0.0001020546378 0.0024281477            0            0 0.0024
##  [46,] -0.0003747528128 0.0083467296            0            0 0.0036
##  [47,] -0.0003045685988 0.0073179930            0            0 0.0028
##  [48,] -0.0001505366505 0.0104927800            0            0 0.0028
##  [49,] -0.0001200889901 0.0051301359            0            0 0.0016
##  [50,] -0.0005102537461 0.0100230600            0            0 0.0032
##  [51,] -0.0004332437989 0.0092964239            0            0 0.0024
##  [52,] -0.0001458250813 0.0039324706            0            0 0.0016
##  [53,] -0.0002747987574 0.0067628026            0            0 0.0024
##  [54,] -0.0002954113512 0.0057792806            0            0 0.0032
##  [55,] -0.0000725516743 0.0026815531            0            0 0.0008
##  [56,]  0.0000169264274 0.0019779155            0            0 0.0016
##  [57,]  0.0001305345087 0.0070166781            0            0 0.0016
##  [58,]  0.0001601214089 0.0059331403            0            0 0.0020
##  [59,] -0.0000484309243 0.0030747339            0            0 0.0012
##  [60,] -0.0004995029758 0.0100749970            0            0 0.0028
##  [61,] -0.0001397710723 0.0039405600            0            0 0.0016
##  [62,] -0.0005631433530 0.0133591318            0            0 0.0040
##  [63,] -0.0007996256009 0.0137450222            0            0 0.0048
##  [64,] -0.0000300575165 0.0010003683            0            0 0.0012
##  [65,]  0.0000000000000 0.0000000000            0            0 0.0000
##  [66,] -0.0003243304752 0.0069584258            0            0 0.0028
##  [67,] -0.0003026812637 0.0060186593            0            0 0.0028
##  [68,] -0.0001000530466 0.0041931781            0            0 0.0032
##  [69,] -0.0002001289925 0.0050504175            0            0 0.0028
##  [70,] -0.0005639484509 0.0121373587            0            0 0.0028
##  [71,]  0.0001037759208 0.0060392970            0            0 0.0024
##  [72,] -0.0001677695224 0.0046879258            0            0 0.0024
##  [73,] -0.0000673156074 0.0021033201            0            0 0.0012
##  [74,] -0.0002837168937 0.0069050370            0            0 0.0024
##  [75,]  0.0000907623925 0.0066024771            0            0 0.0020
##  [76,]  0.0000529449425 0.0030043507            0            0 0.0008
##  [77,] -0.0010191720200 0.0139619469            0            0 0.0060
##  [78,] -0.0003084046769 0.0065656266            0            0 0.0032
##  [79,] -0.0000987579867 0.0035998277            0            0 0.0016
##  [80,] -0.0000606568524 0.0025699701            0            0 0.0008
##  [81,] -0.0003957077732 0.0081596048            0            0 0.0032
##  [82,] -0.0004060014114 0.0073807784            0            0 0.0036
##  [83,] -0.0003029599471 0.0073510181            0            0 0.0040
##  [84,] -0.0000924837699 0.0049309086            0            0 0.0016
##  [85,] -0.0004872016473 0.0089190237            0            0 0.0052
##  [86,] -0.0001069613316 0.0045031814            0            0 0.0016
##  [87,]  0.0000028857398 0.0041322983            0            0 0.0020
##  [88,] -0.0003319425603 0.0069981139            0            0 0.0040
##  [89,]  0.0000511859717 0.0022079397            0            0 0.0008
##  [90,] -0.0000851026343 0.0036052158            0            0 0.0008
##  [91,]  0.0002093433561 0.0073691144            0            0 0.0036
##  [92,] -0.0000418799360 0.0034014392            0            0 0.0020
##  [93,] -0.0003720668971 0.0075541354            0            0 0.0040
##  [94,] -0.0000955632905 0.0030490155            0            0 0.0012
##  [95,] -0.0001262746757 0.0039071987            0            0 0.0016
##  [96,]  0.0001466701540 0.0070801193            0            0 0.0012
##  [97,] -0.0000536395266 0.0033549297            0            0 0.0012
##  [98,]  0.0002635168904 0.0096970037            0            0 0.0032
##  [99,] -0.0001139349156 0.0054544669            0            0 0.0016
## [100,]  0.0000498986888 0.0026699064            0            0 0.0016
## [101,] -0.0003240268991 0.0081177574            0            0 0.0040
## [102,] -0.0000546436030 0.0019334173            0            0 0.0008
## [103,] -0.0002607037385 0.0062257357            0            0 0.0028
## [104,]  0.0002027717289 0.0079107754            0            0 0.0032
## [105,]  0.0001914458798 0.0074062962            0            0 0.0020
## [106,] -0.0001398524223 0.0041377087            0            0 0.0012
## [107,] -0.0001102923373 0.0031709129            0            0 0.0016
## [108,] -0.0003452143057 0.0102498712            0            0 0.0024
## [109,] -0.0001531072587 0.0040030162            0            0 0.0020
## [110,] -0.0003130764811 0.0092524699            0            0 0.0016
## [111,] -0.0001800384167 0.0052766280            0            0 0.0020
## [112,] -0.0003223742082 0.0079391822            0            0 0.0024
## [113,] -0.0001421687959 0.0041819646            0            0 0.0012
## [114,]  0.0003638413089 0.0093730299            0            0 0.0016
## [115,] -0.0001744878048 0.0067134749            0            0 0.0020
## [116,] -0.0002064744935 0.0066785997            0            0 0.0028
## [117,] -0.0001499664939 0.0036420079            0            0 0.0028
## [118,] -0.0004246061606 0.0072163640            0            0 0.0048
## [119,] -0.0001806408383 0.0045642563            0            0 0.0032
## [120,] -0.0003158756561 0.0063944084            0            0 0.0032
## [121,] -0.0001789827315 0.0053398318            0            0 0.0024
## [122,] -0.0005157103872 0.0097127308            0            0 0.0052
## [123,] -0.0003006326854 0.0083086447            0            0 0.0024
## [124,] -0.0002579461877 0.0058814380            0            0 0.0024
## [125,]  0.0004200648050 0.0113102473            0            0 0.0032
## [126,]  0.0001276950637 0.0120096933            0            0 0.0040
## [127,] -0.0000690174496 0.0028426270            0            0 0.0024
## [128,] -0.0002236372263 0.0065508912            0            0 0.0024
## [129,] -0.0002071840026 0.0055858050            0            0 0.0020
## [130,] -0.0000116971060 0.0040317780            0            0 0.0016
## [131,] -0.0012517058751 0.0170697976            0            0 0.0084
## [132,] -0.0019072936159 0.0211683500            0            0 0.0112
## [133,] -0.0005054831540 0.0102625678            0            0 0.0032
## [134,] -0.0002061062083 0.0056494202            0            0 0.0016
## [135,] -0.0006021255642 0.0096296851            0            0 0.0048
## [136,] -0.0003824490149 0.0082821372            0            0 0.0036
## [137,] -0.0000354358860 0.0016072457            0            0 0.0008
## [138,] -0.0002157360687 0.0106312167            0            0 0.0032
## [139,]  0.0000099966057 0.0073421060            0            0 0.0016
## [140,] -0.0001226974246 0.0050659768            0            0 0.0012
## [141,] -0.0002626046751 0.0059638697            0            0 0.0028
## [142,]  0.0001057524433 0.0067480797            0            0 0.0012
## [143,] -0.0003574044163 0.0073629028            0            0 0.0032
## [144,] -0.0001812861793 0.0050857267            0            0 0.0016
## [145,] -0.0002338276145 0.0051277321            0            0 0.0036
## [146,] -0.0000408519211 0.0020425961            0            0 0.0004
## [147,] -0.0000511311478 0.0018075828            0            0 0.0008
## [148,] -0.0002118565939 0.0066348772            0            0 0.0012
## [149,] -0.0000506765349 0.0023956750            0            0 0.0008
## [150,] -0.0000227209774 0.0027544314            0            0 0.0016
## [151,] -0.0000082124367 0.0024058653            0            0 0.0028
## [152,]  0.0000159224292 0.0030496674            0            0 0.0016
## [153,] -0.0000264803704 0.0015567334            0            0 0.0008
## [154,] -0.0000378116076 0.0020365596            0            0 0.0024
## [155,] -0.0014300531739 0.0144341073            0            0 0.0124
## [156,] -0.0001882033814 0.0045091696            0            0 0.0020
## [157,] -0.0001645344626 0.0051147099            0            0 0.0012
## [158,] -0.0006781472124 0.0117522527            0            0 0.0040
## [159,] -0.0055279095032 0.0432175567            0            0 0.0212
## [160,] -0.0001168278872 0.0037910996            0            0 0.0012
## [161,] -0.0010040951319 0.0140106872            0            0 0.0064
## [162,] -0.0009484372392 0.0129589803            0            0 0.0076
## [163,] -0.0000364760509 0.0018141339            0            0 0.0012
## [164,] -0.0000283642029 0.0050076976            0            0 0.0024
## [165,] -0.0001579595138 0.0052186994            0            0 0.0012
## [166,] -0.0007238956012 0.0126764080            0            0 0.0044
## [167,] -0.0002674603393 0.0062380132            0            0 0.0036
## [168,] -0.0003145901499 0.0078539584            0            0 0.0024
## [169,] -0.0005937651225 0.0105368988            0            0 0.0044
## [170,] -0.0000094583730 0.0006629838            0            0 0.0008
## [171,]  0.0000647232773 0.0049078204            0            0 0.0020
## [172,] -0.0000028184191 0.0022345805            0            0 0.0008
## [173,] -0.0000115844362 0.0042967176            0            0 0.0012
## [174,]  0.0000188266149 0.0017366084            0            0 0.0008
## [175,] -0.0001382681933 0.0039680537            0            0 0.0016
## [176,]  0.0000957308901 0.0039725736            0            0 0.0012
## [177,]  0.0002056677385 0.0081780118            0            0 0.0020
## [178,] -0.0001264662756 0.0079513686            0            0 0.0036
## [179,]  0.0000000000000 0.0000000000            0            0 0.0000
## [180,]  0.0000545675325 0.0068734798            0            0 0.0020
## [181,] -0.0003238488978 0.0061188905            0            0 0.0036
## [182,] -0.0001378102478 0.0041570322            0            0 0.0012
## [183,] -0.0000815396707 0.0040769835            0            0 0.0004
## [184,] -0.0002310722681 0.0066484644            0            0 0.0024
## [185,] -0.0000428227080 0.0016992335            0            0 0.0016
## [186,] -0.0006053211220 0.0103328403            0            0 0.0048
## [187,] -0.0007093250417 0.0116413647            0            0 0.0044
## [188,] -0.0001236930019 0.0033347671            0            0 0.0016
## [189,] -0.0000261227146 0.0013061357            0            0 0.0004
## [190,] -0.0003680190176 0.0068832489            0            0 0.0044
## [191,] -0.0001388406572 0.0056931869            0            0 0.0028
## [192,] -0.0001608250851 0.0041039136            0            0 0.0016
## [193,] -0.0007257542169 0.0113756889            0            0 0.0056
## [194,] -0.0001125368287 0.0071616683            0            0 0.0028
## [195,] -0.0001148028412 0.0060025429            0            0 0.0036
## [196,] -0.0002810353801 0.0085344996            0            0 0.0036
## [197,] -0.0001751270166 0.0078503674            0            0 0.0020
## [198,] -0.0001735213528 0.0082121031            0            0 0.0020
## [199,] -0.0005499547777 0.0110736746            0            0 0.0032
## [200,] -0.0005207238105 0.0124029197            0            0 0.0040
## [201,] -0.0001170218219 0.0037076180            0            0 0.0016
## [202,] -0.0013627601745 0.0264890975            0            0 0.0052
## [203,] -0.0000568235199 0.0083337476            0            0 0.0024
## [204,] -0.0002481494126 0.0078173834            0            0 0.0032
## [205,] -0.0006682722609 0.0141030685            0            0 0.0048
## [206,] -0.0006901970702 0.0134428184            0            0 0.0044
## [207,] -0.0004745096605 0.0155932049            0            0 0.0032
## [208,] -0.0000847790687 0.0060486572            0            0 0.0012
## [209,]  0.0001544971816 0.0221166409            0            0 0.0028
## [210,] -0.0004169733006 0.0092547021            0            0 0.0036
## [211,] -0.0004996511864 0.0096419892            0            0 0.0036
## [212,] -0.0002057225914 0.0072024491            0            0 0.0028
## [213,] -0.0002426041357 0.0063110295            0            0 0.0024
## [214,] -0.0001287991305 0.0041108476            0            0 0.0020
## [215,] -0.0000485306715 0.0035450568            0            0 0.0016
## [216,] -0.0003467841483 0.0074728476            0            0 0.0024
## [217,] -0.0002548240529 0.0064973964            0            0 0.0020
## [218,] -0.0000228785333 0.0050676840            0            0 0.0016
## [219,] -0.0016163697211 0.0198059284            0            0 0.0080
## [220,] -0.0025687016084 0.0247410499            0            0 0.0144
## [221,] -0.0003423254932 0.0082575623            0            0 0.0032
## [222,] -0.0003308865171 0.0135397766            0            0 0.0044
## [223,] -0.0003745298887 0.0076732276            0            0 0.0032
## [224,] -0.0006419653464 0.0112783588            0            0 0.0068
## [225,] -0.0004070900378 0.0071979049            0            0 0.0036
## [226,] -0.0008509472949 0.0170261287            0            0 0.0044
## [227,] -0.0002550595151 0.0090477893            0            0 0.0028
## [228,] -0.0003602419471 0.0079081117            0            0 0.0024
## [229,]  0.0007335752432 0.0232858986            0            0 0.0028
## [230,] -0.0014812480333 0.0256283951            0            0 0.0076
## [231,] -0.0069925334184 0.0838365454            0            0 0.0112
## [232,] -0.0009750167832 0.0330173534            0            0 0.0036
## [233,]  0.0000239476601 0.0121241643            0            0 0.0052
## [234,] -0.0025861676000 0.0422076943            0            0 0.0068
## [235,] -0.0004506425698 0.0071452972            0            0 0.0052
## [236,]  0.0000307725611 0.0072164512            0            0 0.0016
## [237,] -0.0002636815601 0.0067783258            0            0 0.0020
## [238,]  0.0000041182899 0.0031257446            0            0 0.0008
## [239,] -0.0005993258348 0.0157463204            0            0 0.0036
## [240,] -0.0013364390579 0.0241499009            0            0 0.0052
## [241,] -0.0000499479692 0.0024973985            0            0 0.0004
## [242,] -0.0002023939755 0.0064156396            0            0 0.0020
## [243,] -0.0006226554071 0.0139607229            0            0 0.0040
## [244,] -0.0005900413855 0.0100360918            0            0 0.0044
## [245,] -0.0002110645749 0.0069665585            0            0 0.0024
## [246,] -0.0001101510375 0.0032683674            0            0 0.0012
## [247,] -0.0001554367329 0.0042371398            0            0 0.0016
## [248,] -0.0003968080406 0.0137394148            0            0 0.0032
## [249,] -0.0000165835102 0.0061526346            0            0 0.0024
## [250,]  0.0006045280034 0.0408870317            0            0 0.0040
## [251,] -0.0003404361898 0.0086897260            0            0 0.0032
## [252,] -0.0007598750678 0.0185165117            0            0 0.0032
## [253,] -0.0000286027514 0.0052893989            0            0 0.0036
## [254,] -0.0003443454414 0.0083923472            0            0 0.0028
## [255,] -0.0006409847845 0.0112197305            0            0 0.0044
## [256,] -0.0001903375220 0.0094373033            0            0 0.0048
## [257,] -0.0010942670322 0.0252251752            0            0 0.0048
## [258,]  0.0003859964748 0.0147098978            0            0 0.0016
## [259,] -0.0003058548320 0.0190917372            0            0 0.0060
## [260,] -0.0001054352106 0.0046511062            0            0 0.0016
## [261,] -0.0000452027083 0.0022601354            0            0 0.0004
## [262,] -0.0000962058313 0.0034893509            0            0 0.0008
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## [264,]  0.0002979350233 0.0188742177            0            0 0.0024
## [265,] -0.0000326221516 0.0019529944            0            0 0.0016
## [266,] -0.0004880171714 0.0147210611            0            0 0.0024
## [267,]  0.0001010774921 0.0076816467            0            0 0.0040
## [268,] -0.0003432472654 0.0068730699            0            0 0.0032
## [269,] -0.0002910940925 0.0074098116            0            0 0.0020
## [270,] -0.0002814248222 0.0085884485            0            0 0.0020
## [271,] -0.0001375622917 0.0060080278            0            0 0.0024
## [272,] -0.0002498921519 0.0052493860            0            0 0.0028
## [273,] -0.0002672923421 0.0077295791            0            0 0.0020
## [274,] -0.0001318261565 0.0052906447            0            0 0.0020
## [275,] -0.0000593931748 0.0076815837            0            0 0.0016
## [276,] -0.0003070526119 0.0077797620            0            0 0.0032
## [277,] -0.0004305563973 0.0085580987            0            0 0.0040
## [278,] -0.0002571498155 0.0068521041            0            0 0.0016
## [279,] -0.0001848541009 0.0046309591            0            0 0.0028
## [280,] -0.0004308593891 0.0107325892            0            0 0.0040
## [281,]  0.0001168431333 0.0178039484            0            0 0.0036
## [282,] -0.0004451237028 0.0130926364            0            0 0.0028
## [283,]  0.0001079462296 0.0114153625            0            0 0.0032
## [284,] -0.0001431001128 0.0071286591            0            0 0.0032
## [285,] -0.0000447644279 0.0084970618            0            0 0.0048
## [286,] -0.0003573171678 0.0071275965            0            0 0.0032
## [287,] -0.0000385239907 0.0075973172            0            0 0.0024
## [288,] -0.0002146871772 0.0053981568            0            0 0.0020
## [289,] -0.0000496814342 0.0018581539            0            0 0.0012
## [290,] -0.0002405766490 0.0060848412            0            0 0.0028
## [291,] -0.0002178654702 0.0082063406            0            0 0.0012
## [292,] -0.0007250924962 0.0113585190            0            0 0.0044
## [293,] -0.0005927171006 0.0221920022            0            0 0.0020
## [294,] -0.0004226246794 0.0109146784            0            0 0.0056
## [295,] -0.0006423922724 0.0130145060            0            0 0.0056
## [296,] -0.0002611764427 0.0071156979            0            0 0.0024
## [297,] -0.0018865643422 0.0241634061            0            0 0.0088
## [298,] -0.0000478002851 0.0057231838            0            0 0.0028
## [299,] -0.0004222734525 0.0104107494            0            0 0.0024
## [300,] -0.0009288980322 0.0140406757            0            0 0.0068
## [301,] -0.0003058029421 0.0073365807            0            0 0.0032
## [302,] -0.0001866287786 0.0049600417            0            0 0.0020
## [303,] -0.0003834679125 0.0124989434            0            0 0.0028
## [304,] -0.0001906133040 0.0117677951            0            0 0.0024
## [305,] -0.0000019353721 0.0066542797            0            0 0.0024
## [306,] -0.0003396702295 0.0086073611            0            0 0.0024
## [307,] -0.0003528402430 0.0077496232            0            0 0.0028
## [308,]  0.0003967768585 0.0239380439            0            0 0.0040
## [309,] -0.0002141446113 0.0063302339            0            0 0.0012
## [310,] -0.0002089881337 0.0053858157            0            0 0.0020
## [311,] -0.0005525402247 0.0156678215            0            0 0.0028
## [312,]  0.0001331407757 0.0049961341            0            0 0.0020
## [313,] -0.0002391931374 0.0077854463            0            0 0.0016
## [314,] -0.0001953764455 0.0044639893            0            0 0.0032
## [315,] -0.0000613256049 0.0078538082            0            0 0.0020
## [316,]  0.0001431309642 0.0080041990            0            0 0.0016
## [317,]  0.0002917078697 0.0116544065            0            0 0.0028
## [318,] -0.0004290656696 0.0081053367            0            0 0.0044
## [319,] -0.0004599716799 0.0080955776            0            0 0.0040
## [320,] -0.0005056837910 0.0094937975            0            0 0.0036
## [321,] -0.0007567813276 0.0130609600            0            0 0.0048
## [322,] -0.0000033306803 0.0027799339            0            0 0.0012
## [323,] -0.0000686204655 0.0030535397            0            0 0.0020
## [324,] -0.0002480443648 0.0064689586            0            0 0.0024
## [325,] -0.0002779404954 0.0073339607            0            0 0.0024
## [326,] -0.0002850097478 0.0057802368            0            0 0.0028
## [327,] -0.0000031254058 0.0001562703            0            0 0.0004
## [328,] -0.0000454468360 0.0024156566            0            0 0.0016
## [329,] -0.0006038050755 0.0121503624            0            0 0.0032
## [330,] -0.0001602275856 0.0118881449            0            0 0.0024
## [331,]  0.0003573676364 0.0336911186            0            0 0.0036
## [332,]  0.0003874902091 0.0220633844            0            0 0.0036
## [333,] -0.0005440854767 0.0111187001            0            0 0.0028
## [334,] -0.0004574756402 0.0093713442            0            0 0.0028
## [335,] -0.0004071524760 0.0079084256            0            0 0.0036
## [336,] -0.0004295929805 0.0161420474            0            0 0.0056
## [337,] -0.0003077644117 0.0079104881            0            0 0.0036
## [338,] -0.0003459735989 0.0075811205            0            0 0.0024
## [339,] -0.0004707188064 0.0099161584            0            0 0.0032
## [340,] -0.0004731829534 0.0089468240            0            0 0.0048
## [341,] -0.0001474418369 0.0038858226            0            0 0.0020
## [342,] -0.0000694898722 0.0067990395            0            0 0.0052
## [343,] -0.0006387653573 0.0132024832            0            0 0.0036
## [344,] -0.0003489349505 0.0099483494            0            0 0.0028
## [345,]  0.0005353459217 0.0206255791            0            0 0.0048
## [346,] -0.0001784389040 0.0056493887            0            0 0.0016
## [347,] -0.0004085866430 0.0084684564            0            0 0.0032
## [348,] -0.0003217241778 0.0086413956            0            0 0.0024
## [349,] -0.0002351468738 0.0048851910            0            0 0.0028
## [350,] -0.0001913616378 0.0052551018            0            0 0.0020
## [351,]  0.0000001990147 0.0037431944            0            0 0.0008
## [352,] -0.0000114985148 0.0048940384            0            0 0.0016
## [353,] -0.0003904918990 0.0089110266            0            0 0.0024
## [354,] -0.0003265122864 0.0078518227            0            0 0.0028
## [355,] -0.0001336346624 0.0054205069            0            0 0.0024
## [356,] -0.0007732953670 0.0128195961            0            0 0.0052
## [357,]  0.0003800048953 0.0220052384            0            0 0.0044
## [358,] -0.0001670521759 0.0064107633            0            0 0.0020
## [359,] -0.0002012375028 0.0119431219            0            0 0.0032
## [360,] -0.0001933084679 0.0060699265            0            0 0.0012
## [361,] -0.0004401857850 0.0095950025            0            0 0.0036
## [362,] -0.0005770967199 0.0114307615            0            0 0.0036
## [363,] -0.0013988805177 0.0348625354            0            0 0.0056
## [364,] -0.0000947394756 0.0060078604            0            0 0.0032
## [365,] -0.0002312124620 0.0061140967            0            0 0.0028
## [366,] -0.0002708699885 0.0062588394            0            0 0.0020
## [367,] -0.0002343194102 0.0054684020            0            0 0.0020
## [368,] -0.0004621110113 0.0103172630            0            0 0.0032
## [369,] -0.0002048766003 0.0053918666            0            0 0.0020
## [370,] -0.0003708990674 0.0079255540            0            0 0.0028
## [371,] -0.0002465349961 0.0063016010            0            0 0.0036
## [372,] -0.0001490083039 0.0047849939            0            0 0.0012
## [373,] -0.0001948356324 0.0054371307            0            0 0.0020
## [374,] -0.0001370279763 0.0060231035            0            0 0.0024
## [375,] -0.0002214722720 0.0067833411            0            0 0.0028
## [376,] -0.0001424070417 0.0045994199            0            0 0.0024
## [377,] -0.0001434686747 0.0048425961            0            0 0.0016
## [378,] -0.0003050949808 0.0078078178            0            0 0.0028
## [379,] -0.0003235403378 0.0068299143            0            0 0.0028
## [380,] -0.0025231548846 0.0256023263            0            0 0.0124
## [381,] -0.0005095480944 0.0092901919            0            0 0.0048
## [382,]  0.0002453771891 0.0065973515            0            0 0.0020
## [383,] -0.0002045575143 0.0074459915            0            0 0.0008
## [384,]  0.0000561188051 0.0060387407            0            0 0.0028
## [385,]  0.0033548447303 0.0705233407            0            0 0.0044
## [386,] -0.0000903749055 0.0028187546            0            0 0.0012
## [387,] -0.0001487835118 0.0062997007            0            0 0.0024
## [388,]  0.0002508915241 0.0133816520            0            0 0.0028
## [389,]  0.0000042434050 0.0047038454            0            0 0.0020
## [390,] -0.0006523812679 0.0151738700            0            0 0.0048
## [391,] -0.0000262362714 0.0091184597            0            0 0.0020
## [392,] -0.0003424567778 0.0100340863            0            0 0.0036
## [393,] -0.0001928472976 0.0065652660            0            0 0.0032
## [394,]  0.0001051131356 0.0072072629            0            0 0.0024
## [395,] -0.0000233878164 0.0015866788            0            0 0.0012
## [396,] -0.0002417590909 0.0061810894            0            0 0.0020
## [397,]  0.0008277790111 0.0264870998            0            0 0.0024
## [398,] -0.0004509331286 0.0093500218            0            0 0.0044
## [399,]  0.0000522273387 0.0133932962            0            0 0.0032
## [400,] -0.0001644965503 0.0065243514            0            0 0.0024
## [401,]  0.0000588294480 0.0219371028            0            0 0.0036
## [402,] -0.0003351184933 0.0074176608            0            0 0.0024
## [403,]  0.0001014199289 0.0048339570            0            0 0.0020
## [404,] -0.0002107725941 0.0064848251            0            0 0.0028
## [405,] -0.0003252646847 0.0068018284            0            0 0.0040
## [406,] -0.0000076196386 0.0011413862            0            0 0.0012
## [407,] -0.0013441963148 0.0150630735            0            0 0.0088
## [408,] -0.0006541512791 0.0108234341            0            0 0.0044
## [409,]  0.0000856702461 0.0048203632            0            0 0.0024
## [410,] -0.0001908953821 0.0064745969            0            0 0.0040
## [411,]  0.0002231188174 0.0109396843            0            0 0.0032
## [412,] -0.0003271333714 0.0064153432            0            0 0.0040
## [413,] -0.0002373285340 0.0103479171            0            0 0.0036
## [414,] -0.0005218044869 0.0174716172            0            0 0.0056
## [415,] -0.0000409573142 0.0084813925            0            0 0.0016
## [416,] -0.0001464235282 0.0052004111            0            0 0.0008
## [417,] -0.0003733203127 0.0099775412            0            0 0.0044
## [418,]  0.0004415618717 0.0175999933            0            0 0.0048
## [419,] -0.0002325578078 0.0052832968            0            0 0.0020
## [420,] -0.0001386727637 0.0055817872            0            0 0.0024
## [421,] -0.0004447531870 0.0114210815            0            0 0.0048
## [422,] -0.0005079637047 0.0108345643            0            0 0.0032
## [423,] -0.0002264185315 0.0053783885            0            0 0.0032
## [424,] -0.0000283357499 0.0051723968            0            0 0.0032
## [425,] -0.0003187741800 0.0074050274            0            0 0.0036
## [426,]  0.0001118703452 0.0076200978            0            0 0.0012
## [427,]  0.0000358793225 0.0071809147            0            0 0.0028
## [428,] -0.0000568986649 0.0088897299            0            0 0.0036
## [429,] -0.0001634146558 0.0038951918            0            0 0.0020
## [430,] -0.0000891436246 0.0032163310            0            0 0.0020
## [431,] -0.0001287276769 0.0062713960            0            0 0.0012
## [432,]  0.0000862310517 0.0035743766            0            0 0.0028
## [433,] -0.0002047701018 0.0056197922            0            0 0.0020
## [434,]  0.0000191871114 0.0022835677            0            0 0.0016
## [435,] -0.0001278116908 0.0038191429            0            0 0.0012
## [436,] -0.0004725178323 0.0098953291            0            0 0.0064
## [437,] -0.0000722575338 0.0111492737            0            0 0.0028
## [438,] -0.0000327724598 0.0020430107            0            0 0.0012
## [439,]  0.0001266296234 0.0151772730            0            0 0.0020
## [440,]  0.0011184739634 0.0431067943            0            0 0.0020
## [441,] -0.0005276780434 0.0106623596            0            0 0.0028
## [442,] -0.0002188261840 0.0070433195            0            0 0.0016
## [443,] -0.0001789026506 0.0061397253            0            0 0.0016
## [444,] -0.0005531511288 0.0324732677            0            0 0.0036
## [445,] -0.0000638477486 0.0055926879            0            0 0.0032
## [446,] -0.0003928826205 0.0083179869            0            0 0.0032
## [447,] -0.0002018062801 0.0094592048            0            0 0.0052
## [448,] -0.0002931417794 0.0059768214            0            0 0.0044
## [449,] -0.0000793306522 0.0062787353            0            0 0.0024
## [450,] -0.0001585218816 0.0080680893            0            0 0.0024
## [451,] -0.0001016399128 0.0102419494            0            0 0.0028
## [452,] -0.0008653812626 0.0156803006            0            0 0.0064
## [453,] -0.0000766289510 0.0095509212            0            0 0.0032
## [454,] -0.0003332360156 0.0068401071            0            0 0.0028
## [455,]  0.0002505551035 0.0148406196            0            0 0.0032
## [456,]  0.0000125199263 0.0119239869            0            0 0.0040
## [457,] -0.0003353127373 0.0077249209            0            0 0.0028
## [458,] -0.0001543634294 0.0052032104            0            0 0.0020
## [459,] -0.0004161903516 0.0084952616            0            0 0.0032
## [460,] -0.0001533369508 0.0059785140            0            0 0.0016
## [461,] -0.0002750589766 0.0066235790            0            0 0.0020
## [462,] -0.0001493970898 0.0047225109            0            0 0.0024
## [463,] -0.0001462399864 0.0046452197            0            0 0.0028
## [464,] -0.0001421169815 0.0076963149            0            0 0.0016
## [465,] -0.0003615375773 0.0075650680            0            0 0.0036
## [466,] -0.0003681778008 0.0125479961            0            0 0.0032
## [467,] -0.0004606970858 0.0142210469            0            0 0.0032
## [468,] -0.0007205710824 0.0141344435            0            0 0.0044
## [469,] -0.0000318269792 0.0013812378            0            0 0.0012
## [470,] -0.0002397112447 0.0056212128            0            0 0.0032
## [471,] -0.0001541085110 0.0055088257            0            0 0.0020
## [472,] -0.0004526815447 0.0122429239            0            0 0.0040
## [473,] -0.0005384340237 0.0093224060            0            0 0.0044
## [474,] -0.0002445794144 0.0060595286            0            0 0.0024
## [475,] -0.0009553638304 0.0168853899            0            0 0.0052
## [476,]  0.0000760275112 0.0065812333            0            0 0.0028
## [477,] -0.0002311791861 0.0064654192            0            0 0.0020
## [478,] -0.0001573891427 0.0044260550            0            0 0.0016
## [479,] -0.0015326729490 0.0212499553            0            0 0.0068
## [480,] -0.0000973813172 0.0037762818            0            0 0.0008
## [481,] -0.0002593710382 0.0062661793            0            0 0.0020
## [482,] -0.0002491105393 0.0072909881            0            0 0.0028
## [483,] -0.0003037467373 0.0065355314            0            0 0.0028
## [484,] -0.0001491252554 0.0049387312            0            0 0.0016
## [485,]  0.0000429027026 0.0037691706            0            0 0.0016
## [486,] -0.0002156622377 0.0094961507            0            0 0.0032
## [487,] -0.0002546418799 0.0061447747            0            0 0.0020
## [488,] -0.0002423088548 0.0050905397            0            0 0.0028
## [489,] -0.0005169058603 0.0097207401            0            0 0.0044
## [490,] -0.0001936680954 0.0049827522            0            0 0.0028
## [491,] -0.0006274750985 0.0104753671            0            0 0.0044
## [492,] -0.0003823083184 0.0073614872            0            0 0.0032
## [493,] -0.0029212618799 0.0535074895            0            0 0.0084
## [494,] -0.0000591528252 0.0029576413            0            0 0.0004
## [495,] -0.0004228779946 0.0085112051            0            0 0.0044
## [496,] -0.0000240759206 0.0053788160            0            0 0.0028
## [497,] -0.0002916896612 0.0085857416            0            0 0.0028
## [498,] -0.0004333908022 0.0100168792            0            0 0.0052
## [499,]  0.0001999355941 0.0120698419            0            0 0.0024
## [500,] -0.0005118718854 0.0093733649            0            0 0.0056
## [501,] -0.0006005119012 0.0134788530            0            0 0.0036
## [502,] -0.0004815499937 0.0093370155            0            0 0.0036
## [503,] -0.0004539452814 0.0090916965            0            0 0.0036
## [504,] -0.0009244514096 0.0142051813            0            0 0.0064
## [505,] -0.0003960822184 0.0079459124            0            0 0.0044
## [506,]  0.0000309363810 0.0069485316            0            0 0.0016
## [507,] -0.0002961878191 0.0070078014            0            0 0.0024
## [508,] -0.0001860789290 0.0052508247            0            0 0.0032
## [509,] -0.0002335790938 0.0046706582            0            0 0.0028
## [510,] -0.0007458897215 0.0118997348            0            0 0.0048
## [511,] -0.0002964392474 0.0068394860            0            0 0.0028
## [512,] -0.0000326079342 0.0013068576            0            0 0.0012
## [513,] -0.0004134917786 0.0089180836            0            0 0.0024
## [514,] -0.0022168078689 0.0275792692            0            0 0.0096
## [515,] -0.0001732648223 0.0085361709            0            0 0.0028
## [516,] -0.0005684537642 0.0090767831            0            0 0.0052
## [517,] -0.0004441443323 0.0084767440            0            0 0.0036
## [518,] -0.0003708018616 0.0094045321            0            0 0.0036
## [519,]  0.0000367326159 0.0095288445            0            0 0.0028
## [520,] -0.0019026448600 0.0474763636            0            0 0.0080
## [521,] -0.0003128234977 0.0072104252            0            0 0.0020
## [522,] -0.0004071825712 0.0134397480            0            0 0.0032
## [523,] -0.0001486793807 0.0038486009            0            0 0.0028
## [524,] -0.0009478386521 0.0137648088            0            0 0.0056
## [525,] -0.0009808472975 0.0308783177            0            0 0.0028
## [526,]  0.0010123029825 0.0255818002            0            0 0.0040
## [527,] -0.0002512089003 0.0065764079            0            0 0.0020
## [528,] -0.0006154968446 0.0128070518            0            0 0.0052
## [529,] -0.0003349490025 0.0096938152            0            0 0.0036
## [530,] -0.0005790830477 0.0101169415            0            0 0.0044
## [531,] -0.0007193672671 0.0124480572            0            0 0.0052
## [532,] -0.0001539425860 0.0036590266            0            0 0.0024
## [533,] -0.0002891631306 0.0070819567            0            0 0.0020
## [534,] -0.0003406445763 0.0081000750            0            0 0.0036
## [535,] -0.0004515787267 0.0101748858            0            0 0.0028
## [536,] -0.0004684568134 0.0146963503            0            0 0.0024
## [537,] -0.0006751443410 0.0153209876            0            0 0.0036
## [538,] -0.0000725942594 0.0029989094            0            0 0.0012
## [539,] -0.0001943843657 0.0057334844            0            0 0.0012
## [540,] -0.0005364819479 0.0095565098            0            0 0.0044
## [541,] -0.0025672920253 0.0308027599            0            0 0.0108
## [542,] -0.0000810910400 0.0054726278            0            0 0.0012
## [543,] -0.0014745831675 0.0168475995            0            0 0.0092
## [544,] -0.0006361070839 0.0105063702            0            0 0.0048
## [545,]  0.0000408888582 0.0095435633            0            0 0.0028
## [546,] -0.0000696347745 0.0041271822            0            0 0.0024
## [547,] -0.0003016159757 0.0132625073            0            0 0.0016
## [548,] -0.0003787717722 0.0077347549            0            0 0.0036
## [549,]  0.0000452273365 0.0146965567            0            0 0.0028
## [550,] -0.0001839968120 0.0055955480            0            0 0.0016
## [551,] -0.0010246348262 0.0149371419            0            0 0.0072
## [552,] -0.0004855172743 0.0094275504            0            0 0.0040
## [553,] -0.0001992327056 0.0052306775            0            0 0.0016
## [554,] -0.0000076070734 0.0073707705            0            0 0.0028
## [555,] -0.0004891682491 0.0095059204            0            0 0.0040
## [556,] -0.0005629228757 0.0105098874            0            0 0.0040
## [557,] -0.0002284582434 0.0077787061            0            0 0.0028
## [558,] -0.0000735577569 0.0034262648            0            0 0.0020
## [559,] -0.0009263100172 0.0232772170            0            0 0.0064
## [560,]  0.0000536329211 0.0092001225            0            0 0.0024
## [561,] -0.0001151265463 0.0030646943            0            0 0.0024
## [562,] -0.0005018326014 0.0085583665            0            0 0.0052
## [563,] -0.0023649567739 0.0512298088            0            0 0.0084
## [564,] -0.0001080360399 0.0082114783            0            0 0.0028
## [565,] -0.0007649064669 0.0150676668            0            0 0.0044
## [566,] -0.0011768112331 0.0152790460            0            0 0.0072
## [567,] -0.0010541797771 0.0164917435            0            0 0.0060
## [568,] -0.0004216007664 0.0082206023            0            0 0.0036
## [569,] -0.0002533944481 0.0069875311            0            0 0.0020
## [570,] -0.0001039741458 0.0030096012            0            0 0.0012
## [571,] -0.0002156644572 0.0074072955            0            0 0.0032
## [572,] -0.0003036334218 0.0077212829            0            0 0.0024
## [573,] -0.0002931886891 0.0093605161            0            0 0.0040
## [574,] -0.0031158740919 0.0751803851            0            0 0.0048
## [575,] -0.0004469989932 0.0103006719            0            0 0.0036
## [576,] -0.0002178014571 0.0055046149            0            0 0.0032
## [577,] -0.0003440544531 0.0081789127            0            0 0.0024
## [578,] -0.0009992112983 0.0161819434            0            0 0.0056
## [579,] -0.0010931994983 0.0271275150            0            0 0.0040
## [580,] -0.0004587123969 0.0095044139            0            0 0.0028
## [581,] -0.0003643595273 0.0091229579            0            0 0.0048
## [582,] -0.0014422333098 0.0189312001            0            0 0.0080
## [583,] -0.0010645211071 0.0177910177            0            0 0.0060
## [584,] -0.0002038178753 0.0061789097            0            0 0.0032
## [585,] -0.0002587646463 0.0070692299            0            0 0.0020
## [586,] -0.0007416383438 0.0134253834            0            0 0.0052
## [587,] -0.0002006543757 0.0095076174            0            0 0.0028
## [588,] -0.0008205274530 0.0229587509            0            0 0.0028
## [589,] -0.0013501437960 0.0189963061            0            0 0.0068
## [590,] -0.0008507766213 0.0265859188            0            0 0.0048
## [591,] -0.0004224303208 0.0077514921            0            0 0.0032
## [592,] -0.0021636198059 0.0249288167            0            0 0.0108
## [593,] -0.0006398758089 0.0109735626            0            0 0.0056
## [594,] -0.0004923903916 0.0084685295            0            0 0.0052
## [595,] -0.0009679470447 0.0147737972            0            0 0.0060
## [596,] -0.0003581151466 0.0077023425            0            0 0.0028
## [597,] -0.0017422576399 0.0191686767            0            0 0.0096
## [598,] -0.0010295068175 0.0145774980            0            0 0.0060
## [599,] -0.0005020149141 0.0138303580            0            0 0.0044
## [600,] -0.0003396206775 0.0101866969            0            0 0.0048
## [601,] -0.0002507895013 0.0078282020            0            0 0.0016
## [602,] -0.0003107241164 0.0076757743            0            0 0.0024
## [603,] -0.0000825475120 0.0062226831            0            0 0.0020
## [604,] -0.0005915039721 0.0109059865            0            0 0.0056
## [605,] -0.0000394178038 0.0018708763            0            0 0.0008
## [606,]  0.0002231388720 0.0235072648            0            0 0.0040
## [607,] -0.0001105173651 0.0028232652            0            0 0.0016
## [608,] -0.0001188674484 0.0112376418            0            0 0.0032
## [609,] -0.0006410729345 0.0118538515            0            0 0.0048
## [610,] -0.0000885166074 0.0033872809            0            0 0.0012
## [611,] -0.0006583971611 0.0092315187            0            0 0.0060
## [612,]  0.0000331535942 0.0121198416            0            0 0.0052
## [613,] -0.0003519017677 0.0072902719            0            0 0.0040
## [614,] -0.0005442708400 0.0085045082            0            0 0.0056
## [615,] -0.0001106324928 0.0061216149            0            0 0.0024
## [616,] -0.0003883569372 0.0082142719            0            0 0.0028
## [617,] -0.0006500122915 0.0114465379            0            0 0.0052
## [618,] -0.0001901338324 0.0105966084            0            0 0.0028
## [619,] -0.0004942803241 0.0076728560            0            0 0.0052
## [620,] -0.0001394975764 0.0034979612            0            0 0.0024
## [621,] -0.0002521222940 0.0060943986            0            0 0.0020
## [622,] -0.0007444891697 0.0109571650            0            0 0.0068
## [623,] -0.0002939651587 0.0067035078            0            0 0.0032
## [624,] -0.0007639580848 0.0123059969            0            0 0.0044
## [625,] -0.0004354051236 0.0080887887            0            0 0.0036
## [626,] -0.0001260526871 0.0043520064            0            0 0.0024
## [627,]  0.0000609914917 0.0075923944            0            0 0.0028
## [628,] -0.0012146952887 0.0421256866            0            0 0.0052
## [629,] -0.0003725524441 0.0080505744            0            0 0.0024
## [630,] -0.0003125111588 0.0094986005            0            0 0.0028
## [631,]  0.0000434165783 0.0158067105            0            0 0.0040
## [632,] -0.0011591276776 0.0184460863            0            0 0.0064
## [633,] -0.0003854290197 0.0093107626            0            0 0.0020
## [634,]  0.0003953653056 0.0196281399            0            0 0.0032
## [635,] -0.0005230982705 0.0102037166            0            0 0.0036
## [636,] -0.0016773911299 0.0294515758            0            0 0.0064
## [637,] -0.0004453215712 0.0086741367            0            0 0.0036
## [638,] -0.0005505931425 0.0133351286            0            0 0.0040
## [639,] -0.0003407168032 0.0070169489            0            0 0.0028
## [640,] -0.0005981997772 0.0151084631            0            0 0.0056
## [641,] -0.0004197869045 0.0120446606            0            0 0.0052
## [642,] -0.0003799972881 0.0082375485            0            0 0.0028
## [643,] -0.0000126328579 0.0050522904            0            0 0.0016
## [644,] -0.0011468566084 0.0204591688            0            0 0.0052
## [645,] -0.0005271498782 0.0091592952            0            0 0.0048
## [646,] -0.0004117705586 0.0079575066            0            0 0.0044
## [647,] -0.0002610676687 0.0063330922            0            0 0.0020
## [648,] -0.0014111516336 0.0255021580            0            0 0.0068
## [649,] -0.0005795696980 0.0107535884            0            0 0.0044
## [650,] -0.0002398621582 0.0072036865            0            0 0.0032
## [651,] -0.0016046515382 0.0258154401            0            0 0.0064
## [652,] -0.0003915183411 0.0079059105            0            0 0.0032
## [653,] -0.0001383473850 0.0041730428            0            0 0.0020
## [654,] -0.0003198334585 0.0108386682            0            0 0.0016
## [655,] -0.0004277522796 0.0090951512            0            0 0.0024
## [656,] -0.0003295075370 0.0071500134            0            0 0.0032
## [657,] -0.0000513906770 0.0053324354            0            0 0.0020
## [658,] -0.0006255631058 0.0146364003            0            0 0.0032
## [659,] -0.0000201493719 0.0077072032            0            0 0.0028
## [660,] -0.0003317521673 0.0113406510            0            0 0.0044
## [661,]  0.0009074410949 0.0255243125            0            0 0.0024
## [662,] -0.0002441865886 0.0063093893            0            0 0.0024
## [663,] -0.0006085573943 0.0143737093            0            0 0.0032
## [664,] -0.0001149194613 0.0041075850            0            0 0.0008
## [665,] -0.0003166161328 0.0071923476            0            0 0.0032
## [666,] -0.0001151702110 0.0058683007            0            0 0.0020
## [667,] -0.0005233636379 0.0142265983            0            0 0.0048
## [668,] -0.0000053129604 0.0092791531            0            0 0.0012
## [669,] -0.0003175909956 0.0079801621            0            0 0.0028
## [670,] -0.0002703436664 0.0085590960            0            0 0.0028
## [671,] -0.0007669881213 0.0116915599            0            0 0.0048
## [672,] -0.0003299400590 0.0071931455            0            0 0.0028
## [673,] -0.0002612451666 0.0060137098            0            0 0.0032
## [674,] -0.0001487571942 0.0037781861            0            0 0.0028
## [675,] -0.0003580591523 0.0083387441            0            0 0.0020
## [676,] -0.0001124565844 0.0043949104            0            0 0.0016
## [677,] -0.0000621308371 0.0031065419            0            0 0.0004
## [678,] -0.0013609235045 0.0214463204            0            0 0.0076
## [679,] -0.0008382995363 0.0125213808            0            0 0.0060
## [680,] -0.0000948155485 0.0028019125            0            0 0.0012
## [681,] -0.0000042265281 0.0051297811            0            0 0.0016
## [682,] -0.0001661721218 0.0042626567            0            0 0.0024
## [683,] -0.0004955277275 0.0091639281            0            0 0.0040
## [684,] -0.0000330971490 0.0091535987            0            0 0.0032
## [685,] -0.0000896187516 0.0046881411            0            0 0.0020
## [686,] -0.0000794975622 0.0161472298            0            0 0.0056
## [687,] -0.0006988737262 0.0147401937            0            0 0.0040
## [688,]  0.0000547268869 0.0043881547            0            0 0.0008
## [689,] -0.0001032502986 0.0040989244            0            0 0.0020
## [690,] -0.0003928980018 0.0101337719            0            0 0.0048
## [691,] -0.0000219341499 0.0017044708            0            0 0.0012
## [692,] -0.0005522101773 0.0095731837            0            0 0.0040
## [693,] -0.0005484332866 0.0133251940            0            0 0.0020
## [694,] -0.0005262667964 0.0115930918            0            0 0.0040
## [695,]  0.0000511064789 0.0060496822            0            0 0.0020
## [696,] -0.0004944387057 0.0101525579            0            0 0.0052
## [697,] -0.0003288029889 0.0088661110            0            0 0.0020
## [698,] -0.0002866064954 0.0105307421            0            0 0.0044
## [699,] -0.0003150744605 0.0069054940            0            0 0.0024
## [700,] -0.0015159811379 0.0194263139            0            0 0.0072
## [701,] -0.0001650360290 0.0046250335            0            0 0.0024
## [702,] -0.0010092205386 0.0140863096            0            0 0.0068
## [703,] -0.0012741231127 0.0167388736            0            0 0.0088
## [704,] -0.0002235016145 0.0073659573            0            0 0.0036
## [705,] -0.0004012466029 0.0070121647            0            0 0.0040
## [706,] -0.0006560036347 0.0114761105            0            0 0.0040
## [707,] -0.0004752664648 0.0114021131            0            0 0.0032
## [708,] -0.0004858543557 0.0127275184            0            0 0.0036
## [709,] -0.0001912200685 0.0064462841            0            0 0.0016
## [710,] -0.0009151765626 0.0174158354            0            0 0.0044
## [711,] -0.0002099192193 0.0061727400            0            0 0.0024
## [712,] -0.0003286975460 0.0152042880            0            0 0.0048
## [713,] -0.0000827674534 0.0097490744            0            0 0.0028
## [714,] -0.0003832078142 0.0098801916            0            0 0.0028
## [715,]  0.0002594942768 0.0083304586            0            0 0.0036
## [716,] -0.0002441485711 0.0064377165            0            0 0.0016
## [717,] -0.0011989836688 0.0168790651            0            0 0.0076
## [718,]  0.0011718260235 0.0238856085            0            0 0.0048
## [719,] -0.0003962820550 0.0080611067            0            0 0.0064
## [720,] -0.0000207088391 0.0105012564            0            0 0.0032
## [721,] -0.0003510195043 0.0060685485            0            0 0.0040
## [722,] -0.0001702141274 0.0089938319            0            0 0.0028
## [723,] -0.0010036300584 0.0181058012            0            0 0.0056
## [724,] -0.0000693031440 0.0054339245            0            0 0.0016
## [725,] -0.0015081004305 0.0547225093            0            0 0.0036
## [726,] -0.0002438961823 0.0068370402            0            0 0.0020
## [727,] -0.0002647618966 0.0066395605            0            0 0.0028
## [728,] -0.0004948329627 0.0084727922            0            0 0.0044
## [729,] -0.0002756928968 0.0076930771            0            0 0.0020
## [730,] -0.0006504164058 0.0097073559            0            0 0.0064

4.3 Fit the NPB model with ozone and temperature, including race/ethnicity

priors.npb <- priors.npb.24

#' Exposures
colnames(X.scaled)
##  [1] "mean_pm"             "mean_o3"             "mean_temp"          
##  [4] "pct_tree_cover"      "pct_impervious"      "mean_aadt_intensity"
##  [7] "dist_m_tri"          "dist_m_npl"          "dist_m_waste_site"  
## [10] "dist_m_major_emit"   "dist_m_cafo"         "dist_m_mine_well"   
## [13] "cvd_rate_adj"        "res_rate_adj"        "violent_crime_rate" 
## [16] "property_crime_rate" "pct_less_hs"         "pct_unemp"          
## [19] "pct_limited_eng"     "pct_hh_pov"          "pct_poc"
#' Covariates
colnames(W.scaled2)
##  [1] "lat"            "lon"            "lat_lon_int"    "latina_re"     
##  [5] "black_re"       "other_re"       "ed_no_hs"       "ed_hs"         
##  [9] "ed_aa"          "ed_4yr"         "low_bmi"        "ovwt_bmi"      
## [13] "obese_bmi"      "concep_spring"  "concep_summer"  "concep_fall"   
## [17] "concep_2010"    "concep_2011"    "concep_2012"    "concep_2013"   
## [21] "maternal_age"   "any_smoker"     "smokeSH"        "mean_cpss"     
## [25] "mean_epsd"      "male"           "days_to_peapod"
# fit.npb2 <- npb(niter = 5000, nburn = 2500, X = X.scaled, Y = Y, W = W.scaled2,
#                scaleY = TRUE,
#                priors = priors.npb, interact = TRUE, XWinteract = TRUE)
# save(fit.npb2, file = here::here("Results", "NPB_Adiposity_v4.2.rdata"))

load(here::here("Results", "NPB_Adiposity_v4.2.rdata"))
npb.sum2 <- summary(fit.npb2)

4.3.1 First, main effect regression coefficients with PIPs

rownames(npb.sum2$main.effects) <- colnames(X.scaled)
npb.sum2$main.effects
##                     Posterior Mean         SD 95% CI Lower 95% CI Upper    PIP
## mean_pm               -0.010554538 0.05903028  -0.16333074   0.11178851 0.3220
## mean_o3               -0.023530384 0.08156296  -0.24121121   0.08924658 0.3632
## mean_temp             -0.013282602 0.07266379  -0.19533371   0.11526919 0.3196
## pct_tree_cover        -0.004871890 0.05652762  -0.14829777   0.11364760 0.2848
## pct_impervious        -0.010040735 0.05058221  -0.15414596   0.08569021 0.2868
## mean_aadt_intensity    0.011691398 0.06471925  -0.07754752   0.21236435 0.2804
## dist_m_tri            -0.010135761 0.05873838  -0.17254024   0.10916930 0.3212
## dist_m_npl            -0.001117706 0.05693107  -0.12758056   0.13773078 0.2952
## dist_m_waste_site      0.027903454 0.09636118  -0.07349430   0.33890726 0.3280
## dist_m_major_emit      0.008850338 0.06691049  -0.08981583   0.19170876 0.2880
## dist_m_cafo           -0.016016807 0.11912587  -0.23751183   0.13747493 0.3500
## dist_m_mine_well      -0.030029747 0.07826655  -0.27154230   0.06711149 0.3772
## cvd_rate_adj          -0.020366856 0.06758799  -0.22109638   0.08446738 0.3488
## res_rate_adj          -0.024713719 0.06863747  -0.21481767   0.04805949 0.3456
## violent_crime_rate    -0.011464748 0.05971514  -0.15773743   0.09280046 0.3152
## property_crime_rate   -0.059763771 0.10534890  -0.34515935   0.03220730 0.4920
## pct_less_hs           -0.014544239 0.06912506  -0.19692052   0.08763224 0.3228
## pct_unemp             -0.034691504 0.09011085  -0.29959460   0.05359022 0.3744
## pct_limited_eng        0.004575868 0.06597523  -0.11695765   0.19130898 0.3060
## pct_hh_pov            -0.021341634 0.06647317  -0.22039649   0.06215629 0.3280
## pct_poc               -0.001717322 0.06092007  -0.12820623   0.14560599 0.2868

4.3.3 Interactions

Next, all of the interactions between exposures or between exposures and covariates

npb.sum2$interactions
##         Posterior Mean          SD 95% CI Lower 95% CI Upper    PIP
##   [1,]  0.000200932651 0.016592127  0.000000000            0 0.0096
##   [2,] -0.000417239433 0.005948661  0.000000000            0 0.0076
##   [3,] -0.002209899186 0.015956065  0.000000000            0 0.0248
##   [4,] -0.004951083674 0.027336154 -0.089701310            0 0.0444
##   [5,] -0.000763524938 0.008360307  0.000000000            0 0.0108
##   [6,] -0.001778670533 0.014551639  0.000000000            0 0.0212
##   [7,] -0.001302053609 0.012922568  0.000000000            0 0.0164
##   [8,] -0.007260017142 0.036857363 -0.129722911            0 0.0532
##   [9,] -0.005250704449 0.029440034 -0.087866714            0 0.0440
##  [10,] -0.002635455586 0.019157660 -0.014506969            0 0.0264
##  [11,] -0.004121048497 0.026173905 -0.070553177            0 0.0340
##  [12,] -0.002043120368 0.016024227  0.000000000            0 0.0220
##  [13,] -0.000849944082 0.009626160  0.000000000            0 0.0120
##  [14,] -0.001802414269 0.014841920  0.000000000            0 0.0188
##  [15,] -0.000520578059 0.007810812  0.000000000            0 0.0080
##  [16,] -0.002648159712 0.019660465  0.000000000            0 0.0256
##  [17,] -0.004316207756 0.026610794 -0.077341251            0 0.0364
##  [18,] -0.008170582676 0.041045525 -0.144403679            0 0.0516
##  [19,] -0.001384151072 0.012105139  0.000000000            0 0.0184
##  [20,] -0.002776660679 0.019802262 -0.028515003            0 0.0260
##  [21,] -0.005074132751 0.027588401 -0.093780229            0 0.0424
##  [22,] -0.000484188150 0.007058413  0.000000000            0 0.0108
##  [23,] -0.000387098595 0.010163467  0.000000000            0 0.0092
##  [24,] -0.000484178439 0.007223877  0.000000000            0 0.0076
##  [25,] -0.003030865651 0.020027521 -0.048526743            0 0.0296
##  [26,] -0.001995043812 0.014417745  0.000000000            0 0.0248
##  [27,] -0.001604794675 0.013548171  0.000000000            0 0.0192
##  [28,] -0.001301150667 0.012846616  0.000000000            0 0.0144
##  [29,] -0.002196075350 0.015468308  0.000000000            0 0.0244
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## [541,] -0.002551167883 0.019108955  0.000000000            0 0.0236
## [542,] -0.002125104959 0.018020334  0.000000000            0 0.0228
## [543,] -0.000526472763 0.023854664  0.000000000            0 0.0116
## [544,] -0.002101314891 0.017833731  0.000000000            0 0.0204
## [545,] -0.001638970247 0.014288610  0.000000000            0 0.0176
## [546,] -0.000716462900 0.012484373  0.000000000            0 0.0132
## [547,] -0.001896091126 0.015980261  0.000000000            0 0.0192
## [548,] -0.002667840964 0.019472661 -0.032550232            0 0.0260
## [549,] -0.001541653493 0.016207597  0.000000000            0 0.0160
## [550,] -0.002958122112 0.022871599  0.000000000            0 0.0244
## [551,] -0.003227441100 0.029306136  0.000000000            0 0.0260
## [552,] -0.001376208672 0.013155157  0.000000000            0 0.0164
## [553,] -0.001122303040 0.011520243  0.000000000            0 0.0156
## [554,] -0.002338947125 0.020317820  0.000000000            0 0.0204
## [555,] -0.000916417111 0.009253832  0.000000000            0 0.0120
## [556,] -0.001649497476 0.013950398  0.000000000            0 0.0188
## [557,] -0.002184607882 0.020578027  0.000000000            0 0.0188
## [558,] -0.001050838638 0.010101100  0.000000000            0 0.0156
## [559,] -0.000966218150 0.009516971  0.000000000            0 0.0132
## [560,] -0.002316936923 0.019682974  0.000000000            0 0.0220
## [561,] -0.005235762913 0.030202041 -0.091184731            0 0.0396
## [562,] -0.001416528421 0.014283032  0.000000000            0 0.0164
## [563,] -0.001751702900 0.014938068  0.000000000            0 0.0180
## [564,] -0.001198003044 0.011660742  0.000000000            0 0.0140
## [565,] -0.002041460858 0.017806718  0.000000000            0 0.0220
## [566,] -0.001177447701 0.012133756  0.000000000            0 0.0152
## [567,] -0.003314356525 0.025129734 -0.040764258            0 0.0304
## [568,] -0.001444925036 0.017128200  0.000000000            0 0.0188
## [569,] -0.002455775675 0.021387634  0.000000000            0 0.0216
## [570,] -0.000966784597 0.010412129  0.000000000            0 0.0124
## [571,] -0.003769989738 0.027156829 -0.060921923            0 0.0300
## [572,] -0.001839536795 0.016278458  0.000000000            0 0.0188
## [573,]  0.000444112223 0.032283430  0.000000000            0 0.0136
## [574,] -0.002401838453 0.020824198  0.000000000            0 0.0212
## [575,] -0.001465703715 0.016136065  0.000000000            0 0.0160
## [576,] -0.001973736281 0.017258374  0.000000000            0 0.0204
## [577,] -0.002057832715 0.017090148  0.000000000            0 0.0220
## [578,] -0.002389904038 0.018422913  0.000000000            0 0.0244
## [579,] -0.001119372887 0.016613708  0.000000000            0 0.0164
## [580,] -0.000951351369 0.009860883  0.000000000            0 0.0140
## [581,] -0.001927585097 0.016484767  0.000000000            0 0.0196
## [582,] -0.001775039893 0.014676654  0.000000000            0 0.0200
## [583,] -0.002076654182 0.021119261  0.000000000            0 0.0200
## [584,] -0.002696130004 0.020772798  0.000000000            0 0.0244
## [585,] -0.001398262790 0.012570546  0.000000000            0 0.0188
## [586,] -0.001504907332 0.012470829  0.000000000            0 0.0188
## [587,] -0.002742334069 0.018813145 -0.026345090            0 0.0268
## [588,] -0.008240741993 0.042731733 -0.129691104            0 0.0560
## [589,] -0.001481605551 0.013840233  0.000000000            0 0.0164
## [590,] -0.006887188526 0.034986811 -0.116682272            0 0.0524
## [591,] -0.003228461196 0.022623789 -0.043102672            0 0.0280
## [592,] -0.000813168627 0.018840316  0.000000000            0 0.0168
## [593,] -0.001500321149 0.013411822  0.000000000            0 0.0164
## [594,] -0.002492603225 0.019581436  0.000000000            0 0.0252
## [595,] -0.002339248372 0.019951885  0.000000000            0 0.0216
## [596,] -0.000773114020 0.015568038  0.000000000            0 0.0144
## [597,] -0.001999033556 0.014961424  0.000000000            0 0.0228
## [598,] -0.004228626004 0.027379888 -0.067155155            0 0.0324
## [599,] -0.004916189886 0.096662317  0.000000000            0 0.0208
## [600,] -0.001500362383 0.013172693  0.000000000            0 0.0164
## [601,] -0.000748977814 0.010631270  0.000000000            0 0.0092
## [602,] -0.003311715191 0.025459296  0.000000000            0 0.0244
## [603,] -0.002983926694 0.020843014 -0.022807969            0 0.0272
## [604,] -0.001579496078 0.014412901  0.000000000            0 0.0176
## [605,] -0.002114419324 0.020531449  0.000000000            0 0.0216
## [606,] -0.003448575615 0.024429173 -0.040001438            0 0.0276
## [607,] -0.001257645653 0.013866839  0.000000000            0 0.0124
## [608,] -0.002685681807 0.019309541  0.000000000            0 0.0252
## [609,] -0.001565934224 0.014673011  0.000000000            0 0.0192
## [610,] -0.002896710606 0.040356124  0.000000000            0 0.0208
## [611,] -0.001296867086 0.014640367  0.000000000            0 0.0168
## [612,] -0.003488353466 0.024240266 -0.048322034            0 0.0280
## [613,] -0.004843374877 0.028617392 -0.081716306            0 0.0376
## [614,] -0.002957842429 0.023930207  0.000000000            0 0.0260
## [615,] -0.003542640377 0.026825675 -0.044273178            0 0.0300
## [616,] -0.001897044428 0.016057653  0.000000000            0 0.0188
## [617,] -0.001188916818 0.010859165  0.000000000            0 0.0140
## [618,] -0.001403305591 0.012779202  0.000000000            0 0.0160
## [619,] -0.002296481977 0.017917157  0.000000000            0 0.0228
## [620,] -0.001576714076 0.013969660  0.000000000            0 0.0168
## [621,] -0.004294410803 0.107327609  0.000000000            0 0.0164
## [622,] -0.000136596945 0.044399976  0.000000000            0 0.0144
## [623,] -0.001458178066 0.016144716  0.000000000            0 0.0172
## [624,] -0.002038053842 0.019364801  0.000000000            0 0.0188
## [625,] -0.003361228384 0.022872376 -0.048156248            0 0.0300
## [626,] -0.002197378476 0.023930528  0.000000000            0 0.0208
## [627,] -0.001659493087 0.016568396  0.000000000            0 0.0172
## [628,] -0.000690943178 0.014303920  0.000000000            0 0.0120
## [629,] -0.004467168701 0.032360623 -0.070593225            0 0.0336
## [630,] -0.004817214717 0.040120921 -0.067987610            0 0.0344
## [631,] -0.000893424553 0.010885265  0.000000000            0 0.0120
## [632,] -0.002538284039 0.018803459  0.000000000            0 0.0248
## [633,] -0.003020022068 0.023579216 -0.008560454            0 0.0260
## [634,] -0.002400614335 0.019846108  0.000000000            0 0.0216
## [635,] -0.003779637966 0.024467038 -0.072673879            0 0.0324
## [636,] -0.005756886486 0.030835012 -0.104446525            0 0.0472
## [637,] -0.002915125081 0.026119737  0.000000000            0 0.0248
## [638,] -0.001928416790 0.018426686  0.000000000            0 0.0180
## [639,] -0.006102895490 0.037721808 -0.095946669            0 0.0404
## [640,] -0.002785471546 0.018506743 -0.042282730            0 0.0308
## [641,] -0.002775946460 0.020151373 -0.020246345            0 0.0264
## [642,] -0.003062313980 0.027539662  0.000000000            0 0.0204
## [643,] -0.000676561935 0.008686938  0.000000000            0 0.0104
## [644,] -0.006174001824 0.033317637 -0.110436386            0 0.0476
## [645,] -0.003934147392 0.025912881 -0.062478852            0 0.0332
## [646,] -0.000928576297 0.011697480  0.000000000            0 0.0104
## [647,] -0.001847919307 0.015422125  0.000000000            0 0.0192
## [648,] -0.001217025705 0.011482556  0.000000000            0 0.0144
## [649,] -0.002289811791 0.023520589  0.000000000            0 0.0196
## [650,] -0.001147313607 0.014916189  0.000000000            0 0.0136
## [651,] -0.001853837200 0.018351995  0.000000000            0 0.0176
## [652,] -0.001436948962 0.014197762  0.000000000            0 0.0152
## [653,] -0.001240785396 0.033129340  0.000000000            0 0.0168
## [654,] -0.001064867702 0.010285178  0.000000000            0 0.0148
## [655,] -0.001248524705 0.013050588  0.000000000            0 0.0136
## [656,] -0.003271887373 0.022977481 -0.049157460            0 0.0288
## [657,] -0.000894136950 0.009915520  0.000000000            0 0.0100
## [658,] -0.001841883108 0.015230362  0.000000000            0 0.0204
## [659,] -0.000712257368 0.013531871  0.000000000            0 0.0104
## [660,] -0.002114636421 0.018045112  0.000000000            0 0.0204
## [661,] -0.001378434278 0.012222340  0.000000000            0 0.0164
## [662,] -0.001437001785 0.014810525  0.000000000            0 0.0148
## [663,] -0.001061959364 0.011190245  0.000000000            0 0.0128
## [664,] -0.002966749305 0.024962998  0.000000000            0 0.0248
## [665,] -0.001839635087 0.015337371  0.000000000            0 0.0188
## [666,] -0.001259841196 0.011359171  0.000000000            0 0.0160
## [667,] -0.001449509943 0.012954402  0.000000000            0 0.0164
## [668,] -0.003511605565 0.026140410 -0.056732529            0 0.0304
## [669,] -0.002855862793 0.019982705 -0.035420297            0 0.0284
## [670,] -0.001377391256 0.013012787  0.000000000            0 0.0172
## [671,] -0.003611686682 0.025340885 -0.049051406            0 0.0300
## [672,] -0.002559426761 0.021224625  0.000000000            0 0.0216
## [673,] -0.002224687207 0.022324240  0.000000000            0 0.0188
## [674,] -0.001119488630 0.010991796  0.000000000            0 0.0136
## [675,] -0.003326631113 0.028502315  0.000000000            0 0.0252
## [676,] -0.002132156509 0.018282459  0.000000000            0 0.0200
## [677,] -0.001645442602 0.016557288  0.000000000            0 0.0180
## [678,] -0.001080372012 0.010499248  0.000000000            0 0.0136
## [679,] -0.003597708808 0.028985658 -0.042305705            0 0.0292
## [680,] -0.002032728566 0.028201603  0.000000000            0 0.0192
## [681,] -0.000392666453 0.018843687  0.000000000            0 0.0132
## [682,] -0.001368380824 0.012670927  0.000000000            0 0.0160
## [683,] -0.004322609307 0.031045909 -0.058727811            0 0.0308
## [684,] -0.001455560731 0.016934423  0.000000000            0 0.0196
## [685,] -0.001864488359 0.014546199  0.000000000            0 0.0236
## [686,] -0.001442148771 0.013394054  0.000000000            0 0.0160
## [687,] -0.002854371311 0.021482624  0.000000000            0 0.0260
## [688,] -0.001105332820 0.012360506  0.000000000            0 0.0140
## [689,] -0.002022390724 0.015589621  0.000000000            0 0.0228
## [690,] -0.001454213628 0.013590255  0.000000000            0 0.0148
## [691,] -0.002254928857 0.017917670  0.000000000            0 0.0224
## [692,] -0.001515559586 0.014091267  0.000000000            0 0.0156
## [693,] -0.002246465475 0.018118800  0.000000000            0 0.0232
## [694,] -0.001398236050 0.012253929  0.000000000            0 0.0172
## [695,] -0.004666866470 0.030747639 -0.081352764            0 0.0368
## [696,] -0.003446185880 0.021683088 -0.061974032            0 0.0332
## [697,] -0.001458545489 0.013641927  0.000000000            0 0.0160
## [698,] -0.005237227210 0.032090797 -0.086269286            0 0.0396
## [699,] -0.002104766608 0.017923831  0.000000000            0 0.0220
## [700,] -0.000998748053 0.011398706  0.000000000            0 0.0132
## [701,] -0.001522911092 0.013551048  0.000000000            0 0.0168
## [702,] -0.002014298590 0.020625917  0.000000000            0 0.0188
## [703,] -0.001636439458 0.016182344  0.000000000            0 0.0152
## [704,] -0.001160966004 0.012690965  0.000000000            0 0.0168
## [705,] -0.001353426401 0.011993056  0.000000000            0 0.0168
## [706,] -0.000466348023 0.012439117  0.000000000            0 0.0120
## [707,] -0.002729307038 0.021734114  0.000000000            0 0.0236
## [708,] -0.000224573576 0.018631667  0.000000000            0 0.0112
## [709,] -0.000801772366 0.009593489  0.000000000            0 0.0100
## [710,] -0.002871321194 0.023180409  0.000000000            0 0.0240
## [711,] -0.001448587962 0.014671867  0.000000000            0 0.0132
## [712,] -0.001569633054 0.013788812  0.000000000            0 0.0152
## [713,] -0.000084139628 0.022137636  0.000000000            0 0.0128
## [714,] -0.001791183042 0.016576771  0.000000000            0 0.0204
## [715,] -0.001166135272 0.011038585  0.000000000            0 0.0160
## [716,] -0.001654114954 0.014996733  0.000000000            0 0.0172
## [717,] -0.001051500765 0.010519977  0.000000000            0 0.0132
## [718,] -0.002515160161 0.020677659  0.000000000            0 0.0252
## [719,] -0.001205537302 0.010796101  0.000000000            0 0.0152
## [720,] -0.001491676756 0.013510236  0.000000000            0 0.0184
## [721,] -0.001070300825 0.010869983  0.000000000            0 0.0136
## [722,] -0.001539930563 0.014438024  0.000000000            0 0.0180
## [723,] -0.001196460676 0.011795563  0.000000000            0 0.0136
## [724,] -0.001515873535 0.014014958  0.000000000            0 0.0152
## [725,] -0.003399083012 0.021568979 -0.047850389            0 0.0340
## [726,] -0.002755370323 0.022618981  0.000000000            0 0.0220
## [727,] -0.000860488517 0.010017921  0.000000000            0 0.0132
## [728,] -0.001107961287 0.013603288  0.000000000            0 0.0120
## [729,] -0.001806163001 0.016093696  0.000000000            0 0.0192
## [730,] -0.002135021788 0.016506656  0.000000000            0 0.0232
## [731,] -0.001074515462 0.011116523  0.000000000            0 0.0140
## [732,] -0.002191157050 0.019301357  0.000000000            0 0.0240
## [733,] -0.001863221347 0.015537532  0.000000000            0 0.0236
## [734,] -0.002445686880 0.018903981  0.000000000            0 0.0232
## [735,] -0.001009014042 0.010466014  0.000000000            0 0.0128
## [736,] -0.000898468320 0.010808528  0.000000000            0 0.0112
## [737,] -0.002286490026 0.017423190  0.000000000            0 0.0240
## [738,] -0.001208216462 0.013319360  0.000000000            0 0.0148
## [739,] -0.003900564801 0.030180685 -0.050958622            0 0.0292
## [740,] -0.002758464403 0.021433569 -0.021833707            0 0.0280
## [741,] -0.001867016433 0.015846165  0.000000000            0 0.0184
## [742,] -0.001134296535 0.013696975  0.000000000            0 0.0136
## [743,] -0.002154757650 0.019035408  0.000000000            0 0.0200
## [744,] -0.001229940992 0.013022243  0.000000000            0 0.0140
## [745,] -0.002315205442 0.020512701  0.000000000            0 0.0228
## [746,] -0.002213009525 0.018385090  0.000000000            0 0.0204
## [747,] -0.003552733066 0.021878727 -0.065332991            0 0.0320
## [748,] -0.001854739383 0.013486054  0.000000000            0 0.0224
## [749,] -0.004158913248 0.028113151 -0.064572818            0 0.0328
## [750,] -0.004739238321 0.028300050 -0.081011856            0 0.0392
## [751,] -0.001215836299 0.011772638  0.000000000            0 0.0156
## [752,] -0.002867396635 0.019785976 -0.046990064            0 0.0284
## [753,] -0.002842023612 0.022158623 -0.031124386            0 0.0276
## [754,] -0.001032344628 0.010488587  0.000000000            0 0.0140
## [755,] -0.001431813039 0.014002182  0.000000000            0 0.0168
## [756,] -0.001743843020 0.016548575  0.000000000            0 0.0184
## [757,] -0.002559551559 0.018909407  0.000000000            0 0.0240
## [758,] -0.001464013802 0.015933172  0.000000000            0 0.0160
## [759,] -0.000941214676 0.010516382  0.000000000            0 0.0116
## [760,] -0.001265758585 0.012268412  0.000000000            0 0.0140
## [761,] -0.001784309742 0.017072805  0.000000000            0 0.0164
## [762,] -0.001075238481 0.013336445  0.000000000            0 0.0112
## [763,] -0.001514307986 0.013848726  0.000000000            0 0.0156
## [764,] -0.003556564322 0.024044291 -0.054830614            0 0.0304
## [765,]  0.000779691560 0.035446358  0.000000000            0 0.0080
## [766,] -0.002512467615 0.018231914  0.000000000            0 0.0252
## [767,] -0.000777365458 0.014229808  0.000000000            0 0.0152
## [768,] -0.001647301563 0.018719264  0.000000000            0 0.0172
## [769,] -0.001206339221 0.012861724  0.000000000            0 0.0144
## [770,] -0.003013006649 0.024662032 -0.019485114            0 0.0268
## [771,] -0.001100007972 0.010445468  0.000000000            0 0.0152
## [772,] -0.003251109148 0.030860728  0.000000000            0 0.0212
## [773,] -0.002004827286 0.017827829  0.000000000            0 0.0188
## [774,] -0.001152901258 0.010194215  0.000000000            0 0.0164
## [775,] -0.001231707633 0.013570668  0.000000000            0 0.0120
## [776,] -0.002572007939 0.020403281  0.000000000            0 0.0236
## [777,] -0.002776826858 0.019970924 -0.024102091            0 0.0280

4.4 Fit the NPB model with ozone, excluding race/ethnicity

Because race/ethnicity might be on the causal pathway (mediator), we want to see if anything shows up when we exclude those variables from the model

priors.npb <- priors.npb.24

#' Exposures
colnames(X.scaled)
##  [1] "mean_pm"             "mean_o3"             "mean_temp"          
##  [4] "pct_tree_cover"      "pct_impervious"      "mean_aadt_intensity"
##  [7] "dist_m_tri"          "dist_m_npl"          "dist_m_waste_site"  
## [10] "dist_m_major_emit"   "dist_m_cafo"         "dist_m_mine_well"   
## [13] "cvd_rate_adj"        "res_rate_adj"        "violent_crime_rate" 
## [16] "property_crime_rate" "pct_less_hs"         "pct_unemp"          
## [19] "pct_limited_eng"     "pct_hh_pov"          "pct_poc"
#' Covariates
colnames(W.scaled2)
##  [1] "lat"            "lon"            "lat_lon_int"    "latina_re"     
##  [5] "black_re"       "other_re"       "ed_no_hs"       "ed_hs"         
##  [9] "ed_aa"          "ed_4yr"         "low_bmi"        "ovwt_bmi"      
## [13] "obese_bmi"      "concep_spring"  "concep_summer"  "concep_fall"   
## [17] "concep_2010"    "concep_2011"    "concep_2012"    "concep_2013"   
## [21] "maternal_age"   "any_smoker"     "smokeSH"        "mean_cpss"     
## [25] "mean_epsd"      "male"           "days_to_peapod"
# fit.npb3 <- npb(niter = 5000, nburn = 2500, X = X.scaled[,-c(3)], Y = Y, W = W.scaled2[,-c(4:6)],
#                scaleY = TRUE,
#                priors = priors.npb, interact = TRUE, XWinteract = TRUE)
# save(fit.npb3, file = here::here("Results", "NPB_Adiposity_v4a.1.rdata"))

load(here::here("Results", "NPB_Adiposity_v4a.1.rdata"))
npb.sum3 <- summary(fit.npb3)

4.4.1 First, main effect regression coefficients with PIPs

rownames(npb.sum3$main.effects) <- colnames(X.scaled[,-c(3)])
npb.sum3$main.effects
##                     Posterior Mean         SD 95% CI Lower 95% CI Upper    PIP
## mean_pm               -0.012631762 0.05528734  -0.16865861   0.07729421 0.2676
## mean_o3               -0.034175779 0.08978837  -0.27926198   0.05982863 0.3592
## pct_tree_cover        -0.008806492 0.05449876  -0.15798453   0.09438554 0.2580
## pct_impervious        -0.015696129 0.05739704  -0.17754353   0.05755177 0.2716
## mean_aadt_intensity    0.011216799 0.06452326  -0.08090708   0.22588466 0.2424
## dist_m_tri            -0.013271220 0.05910733  -0.16694697   0.09109124 0.2876
## dist_m_npl            -0.004693099 0.05488418  -0.13719647   0.12539949 0.2536
## dist_m_waste_site      0.028018679 0.09889330  -0.07327447   0.36237371 0.2844
## dist_m_major_emit      0.001054655 0.05324843  -0.10776088   0.14801417 0.2316
## dist_m_cafo           -0.019398321 0.10014041  -0.24332798   0.11522828 0.3160
## dist_m_mine_well      -0.035643689 0.08414809  -0.25890102   0.04895471 0.3656
## cvd_rate_adj          -0.028467006 0.07506970  -0.24624291   0.04341892 0.3352
## res_rate_adj          -0.030021658 0.07570491  -0.26084700   0.04621521 0.3408
## violent_crime_rate    -0.015966384 0.05377350  -0.16337898   0.05514798 0.2880
## property_crime_rate   -0.070054166 0.11175110  -0.36720111   0.01610051 0.4932
## pct_less_hs           -0.025306998 0.07520270  -0.24662765   0.05368069 0.3148
## pct_unemp             -0.046480601 0.09710954  -0.34433680   0.02897601 0.3864
## pct_limited_eng        0.000138379 0.06537619  -0.12528219   0.16858018 0.2612
## pct_hh_pov            -0.028241196 0.07842328  -0.25016808   0.04726586 0.3216
## pct_poc               -0.005169879 0.06528859  -0.15475411   0.13224523 0.2604
npb.sum3$main.effects$exp <- rownames(npb.sum3$main.effects)
## Warning in npb.sum3$main.effects$exp <- rownames(npb.sum3$main.effects):
## Coercing LHS to a list
write_csv(as.data.frame(npb.sum3$main.effects), here::here("Results", "NPB_Main_Effects_Adiposity_v4a.csv"))

4.4.3 Interactions

Next, all of the interactions between exposures or between exposures and covariates

npb.sum3$interactions
##         Posterior Mean          SD 95% CI Lower 95% CI Upper    PIP
##   [1,]  0.000007369012 0.007785004   0.00000000            0 0.0040
##   [2,] -0.001087185637 0.011445499   0.00000000            0 0.0116
##   [3,] -0.003859248800 0.026494688  -0.03914222            0 0.0296
##   [4,] -0.000343655421 0.007567538   0.00000000            0 0.0044
##   [5,] -0.000495833664 0.007665230   0.00000000            0 0.0076
##   [6,] -0.000706795560 0.008687952   0.00000000            0 0.0088
##   [7,] -0.004573708763 0.030147252  -0.06402255            0 0.0304
##   [8,] -0.003235470019 0.026098313   0.00000000            0 0.0212
##   [9,] -0.001554260470 0.014682955   0.00000000            0 0.0148
##  [10,] -0.001707048981 0.014642520   0.00000000            0 0.0172
##  [11,] -0.001082329141 0.011542653   0.00000000            0 0.0124
##  [12,] -0.000568599567 0.009724079   0.00000000            0 0.0092
##  [13,] -0.000509434550 0.007752006   0.00000000            0 0.0060
##  [14,] -0.000551156430 0.007672694   0.00000000            0 0.0076
##  [15,] -0.002354826900 0.020096119   0.00000000            0 0.0208
##  [16,] -0.002183197736 0.020153000   0.00000000            0 0.0196
##  [17,] -0.003906072546 0.027663953  -0.03639852            0 0.0272
##  [18,] -0.000867730308 0.010553016   0.00000000            0 0.0112
##  [19,] -0.001155643381 0.013407614   0.00000000            0 0.0120
##  [20,] -0.000689731704 0.008837173   0.00000000            0 0.0096
##  [21,] -0.000295983374 0.007129817   0.00000000            0 0.0080
##  [22,] -0.000336119011 0.005270125   0.00000000            0 0.0048
##  [23,] -0.002631918077 0.022244416   0.00000000            0 0.0192
##  [24,] -0.000951145801 0.010181161   0.00000000            0 0.0116
##  [25,] -0.001075157094 0.012498368   0.00000000            0 0.0120
##  [26,] -0.001134240818 0.012176631   0.00000000            0 0.0136
##  [27,] -0.001670493825 0.015491508   0.00000000            0 0.0156
##  [28,] -0.001083073340 0.011687012   0.00000000            0 0.0144
##  [29,] -0.000334112249 0.006128716   0.00000000            0 0.0052
##  [30,] -0.000188054069 0.005409133   0.00000000            0 0.0052
##  [31,] -0.000160919850 0.004541450   0.00000000            0 0.0060
##  [32,] -0.000133410178 0.003048737   0.00000000            0 0.0036
##  [33,] -0.001077500621 0.012335497   0.00000000            0 0.0108
##  [34,] -0.001013471496 0.010965478   0.00000000            0 0.0108
##  [35,] -0.001171112068 0.012906853   0.00000000            0 0.0104
##  [36,] -0.000237453579 0.006027415   0.00000000            0 0.0076
##  [37,] -0.001642430405 0.016883565   0.00000000            0 0.0164
##  [38,] -0.000301997014 0.006520882   0.00000000            0 0.0076
##  [39,] -0.000419401469 0.008622383   0.00000000            0 0.0064
##  [40,] -0.000643937226 0.007912578   0.00000000            0 0.0112
##  [41,] -0.000616892821 0.007391041   0.00000000            0 0.0088
##  [42,] -0.000466932176 0.007768467   0.00000000            0 0.0076
##  [43,]  0.000058730857 0.010033782   0.00000000            0 0.0068
##  [44,] -0.000673744652 0.008169369   0.00000000            0 0.0096
##  [45,] -0.000519171424 0.008328063   0.00000000            0 0.0080
##  [46,] -0.000570042776 0.008465747   0.00000000            0 0.0072
##  [47,] -0.001008578991 0.012111314   0.00000000            0 0.0096
##  [48,] -0.000548506650 0.008538699   0.00000000            0 0.0084
##  [49,] -0.000378415808 0.005843082   0.00000000            0 0.0060
##  [50,] -0.001179248038 0.013561568   0.00000000            0 0.0144
##  [51,] -0.000884918397 0.012109211   0.00000000            0 0.0096
##  [52,] -0.000640908862 0.008790442   0.00000000            0 0.0088
##  [53,] -0.000481219533 0.007425474   0.00000000            0 0.0056
##  [54,] -0.001023386148 0.011652120   0.00000000            0 0.0128
##  [55,] -0.000229186273 0.005324289   0.00000000            0 0.0048
##  [56,] -0.000044378964 0.002563201   0.00000000            0 0.0032
##  [57,] -0.000194187112 0.003984706   0.00000000            0 0.0032
##  [58,] -0.000072096773 0.003952996   0.00000000            0 0.0048
##  [59,] -0.000222438940 0.006358297   0.00000000            0 0.0064
##  [60,] -0.000465856387 0.007311785   0.00000000            0 0.0068
##  [61,] -0.000507249524 0.008615512   0.00000000            0 0.0068
##  [62,] -0.002010224992 0.017484110   0.00000000            0 0.0196
##  [63,] -0.002766052858 0.020736591   0.00000000            0 0.0244
##  [64,] -0.000264651539 0.004816263   0.00000000            0 0.0064
##  [65,] -0.000347684190 0.005122497   0.00000000            0 0.0056
##  [66,] -0.001032462761 0.011133324   0.00000000            0 0.0124
##  [67,] -0.001182624247 0.011603311   0.00000000            0 0.0144
##  [68,] -0.000372019511 0.006330552   0.00000000            0 0.0064
##  [69,] -0.000657901070 0.008531269   0.00000000            0 0.0092
##  [70,] -0.001057676500 0.012166526   0.00000000            0 0.0120
##  [71,] -0.000475143676 0.006845651   0.00000000            0 0.0060
##  [72,] -0.000439326569 0.006753164   0.00000000            0 0.0068
##  [73,] -0.000092949948 0.004185770   0.00000000            0 0.0048
##  [74,] -0.001121285608 0.012652721   0.00000000            0 0.0132
##  [75,] -0.000163110431 0.005258528   0.00000000            0 0.0040
##  [76,] -0.000666583248 0.007824870   0.00000000            0 0.0108
##  [77,] -0.001752020000 0.016236983   0.00000000            0 0.0160
##  [78,] -0.001495399865 0.015946314   0.00000000            0 0.0140
##  [79,] -0.001099754674 0.012928164   0.00000000            0 0.0124
##  [80,] -0.000066877006 0.007365214   0.00000000            0 0.0076
##  [81,] -0.001516897940 0.015429205   0.00000000            0 0.0172
##  [82,] -0.001176673921 0.013441634   0.00000000            0 0.0140
##  [83,] -0.000718522373 0.011233008   0.00000000            0 0.0100
##  [84,] -0.000616854365 0.011635386   0.00000000            0 0.0100
##  [85,] -0.001143846694 0.011883260   0.00000000            0 0.0136
##  [86,] -0.000875370694 0.009556649   0.00000000            0 0.0116
##  [87,] -0.000750211127 0.011014890   0.00000000            0 0.0100
##  [88,] -0.000741614158 0.009264901   0.00000000            0 0.0088
##  [89,] -0.000386150919 0.006657330   0.00000000            0 0.0056
##  [90,] -0.000204521859 0.009110889   0.00000000            0 0.0068
##  [91,] -0.000293247879 0.005765034   0.00000000            0 0.0052
##  [92,] -0.000282352304 0.005149325   0.00000000            0 0.0068
##  [93,] -0.001138716852 0.011304737   0.00000000            0 0.0152
##  [94,] -0.001266011357 0.011942801   0.00000000            0 0.0156
##  [95,] -0.000397613945 0.005508615   0.00000000            0 0.0088
##  [96,]  0.000087079693 0.013488916   0.00000000            0 0.0048
##  [97,] -0.000283324406 0.008754581   0.00000000            0 0.0084
##  [98,] -0.000244261037 0.007720834   0.00000000            0 0.0064
##  [99,] -0.000433145631 0.006846121   0.00000000            0 0.0052
## [100,] -0.000580887863 0.011527986   0.00000000            0 0.0100
## [101,] -0.000950631524 0.011609665   0.00000000            0 0.0104
## [102,] -0.000276464930 0.009732937   0.00000000            0 0.0064
## [103,] -0.000771413255 0.009548917   0.00000000            0 0.0116
## [104,] -0.000154302220 0.003630637   0.00000000            0 0.0044
## [105,] -0.000187755298 0.004938637   0.00000000            0 0.0032
## [106,] -0.000589043759 0.008493988   0.00000000            0 0.0068
## [107,] -0.000463323534 0.007080863   0.00000000            0 0.0064
## [108,] -0.000834812997 0.010219080   0.00000000            0 0.0096
## [109,] -0.000240057116 0.006519918   0.00000000            0 0.0048
## [110,] -0.001213796269 0.012604336   0.00000000            0 0.0128
## [111,] -0.000540787002 0.008119992   0.00000000            0 0.0096
## [112,] -0.000343575048 0.005591067   0.00000000            0 0.0060
## [113,] -0.000778985472 0.009081388   0.00000000            0 0.0100
## [114,]  0.000302931124 0.012134740   0.00000000            0 0.0052
## [115,] -0.000736181526 0.011256503   0.00000000            0 0.0100
## [116,] -0.000845135715 0.010682288   0.00000000            0 0.0100
## [117,] -0.001176187893 0.014308958   0.00000000            0 0.0112
## [118,] -0.001635107136 0.018685322   0.00000000            0 0.0136
## [119,] -0.000705353961 0.009970485   0.00000000            0 0.0092
## [120,] -0.000956057522 0.012182396   0.00000000            0 0.0108
## [121,] -0.000346680507 0.007338784   0.00000000            0 0.0084
## [122,] -0.000834373482 0.009856706   0.00000000            0 0.0116
## [123,] -0.000355320381 0.006853749   0.00000000            0 0.0060
## [124,] -0.001117229635 0.012249560   0.00000000            0 0.0116
## [125,]  0.000042347968 0.007653013   0.00000000            0 0.0036
## [126,] -0.000317663223 0.008373776   0.00000000            0 0.0060
## [127,] -0.000553318610 0.007880219   0.00000000            0 0.0088
## [128,] -0.000469732137 0.010146412   0.00000000            0 0.0084
## [129,] -0.000838411642 0.008752937   0.00000000            0 0.0124
## [130,] -0.000395586737 0.008069839   0.00000000            0 0.0072
## [131,] -0.002709334721 0.022138944   0.00000000            0 0.0208
## [132,] -0.002962443558 0.022495935   0.00000000            0 0.0252
## [133,] -0.001203005725 0.014461196   0.00000000            0 0.0100
## [134,] -0.000532823026 0.007880343   0.00000000            0 0.0084
## [135,] -0.002152094701 0.018434504   0.00000000            0 0.0188
## [136,] -0.001023367549 0.011138389   0.00000000            0 0.0140
## [137,] -0.000668625660 0.007937444   0.00000000            0 0.0108
## [138,] -0.000966608270 0.011678858   0.00000000            0 0.0108
## [139,] -0.000495813868 0.007620320   0.00000000            0 0.0072
## [140,] -0.000616136229 0.008322468   0.00000000            0 0.0068
## [141,] -0.000559038092 0.008101018   0.00000000            0 0.0072
## [142,] -0.000878568545 0.011335108   0.00000000            0 0.0112
## [143,] -0.001088747754 0.012223008   0.00000000            0 0.0108
## [144,] -0.000633849657 0.008418216   0.00000000            0 0.0084
## [145,] -0.000980681727 0.011801631   0.00000000            0 0.0100
## [146,] -0.000151467778 0.006118941   0.00000000            0 0.0068
## [147,] -0.000164166782 0.004424244   0.00000000            0 0.0064
## [148,] -0.000604537236 0.008130696   0.00000000            0 0.0128
## [149,] -0.000269722103 0.010486138   0.00000000            0 0.0080
## [150,] -0.000549261856 0.009858245   0.00000000            0 0.0056
## [151,] -0.000195473236 0.010126083   0.00000000            0 0.0064
## [152,] -0.000702178095 0.009193287   0.00000000            0 0.0080
## [153,] -0.000437215032 0.006843770   0.00000000            0 0.0056
## [154,] -0.000447166647 0.007690697   0.00000000            0 0.0076
## [155,] -0.003238349245 0.021462852  -0.04990976            0 0.0288
## [156,] -0.001086064660 0.011925809   0.00000000            0 0.0124
## [157,] -0.000912651883 0.010753528   0.00000000            0 0.0100
## [158,] -0.001591459864 0.015491332   0.00000000            0 0.0152
## [159,] -0.011205322977 0.058432686  -0.19643005            0 0.0556
## [160,] -0.000696814364 0.010872207   0.00000000            0 0.0076
## [161,] -0.001486669392 0.013905783   0.00000000            0 0.0168
## [162,] -0.002140362698 0.017445957   0.00000000            0 0.0208
## [163,] -0.000280651379 0.004821569   0.00000000            0 0.0044
## [164,] -0.000310678207 0.005138752   0.00000000            0 0.0064
## [165,] -0.000954460838 0.011232236   0.00000000            0 0.0116
## [166,] -0.001790815388 0.019756911   0.00000000            0 0.0140
## [167,] -0.000835241633 0.011087229   0.00000000            0 0.0092
## [168,] -0.001339058957 0.014282890   0.00000000            0 0.0112
## [169,] -0.001372088963 0.014869602   0.00000000            0 0.0120
## [170,] -0.000046073019 0.001556375   0.00000000            0 0.0012
## [171,] -0.000160902428 0.003262978   0.00000000            0 0.0028
## [172,] -0.000154574245 0.005560609   0.00000000            0 0.0044
## [173,] -0.000286844514 0.005929387   0.00000000            0 0.0052
## [174,] -0.000046764673 0.002169896   0.00000000            0 0.0032
## [175,] -0.000191914711 0.006183322   0.00000000            0 0.0072
## [176,] -0.000028344376 0.007570389   0.00000000            0 0.0040
## [177,] -0.000049024107 0.005941999   0.00000000            0 0.0040
## [178,] -0.000148221114 0.003296643   0.00000000            0 0.0024
## [179,] -0.000226494441 0.007136060   0.00000000            0 0.0044
## [180,] -0.000173342042 0.003908216   0.00000000            0 0.0036
## [181,] -0.000846752481 0.010112200   0.00000000            0 0.0092
## [182,] -0.000394853745 0.006089181   0.00000000            0 0.0068
## [183,] -0.000290303575 0.004637215   0.00000000            0 0.0080
## [184,] -0.000940893938 0.012133002   0.00000000            0 0.0132
## [185,] -0.001069679500 0.011358509   0.00000000            0 0.0116
## [186,] -0.000682309044 0.009494861   0.00000000            0 0.0080
## [187,] -0.002611660248 0.020965300   0.00000000            0 0.0208
## [188,] -0.000251849135 0.004586055   0.00000000            0 0.0060
## [189,] -0.000424047277 0.006078313   0.00000000            0 0.0056
## [190,] -0.000599008144 0.006507759   0.00000000            0 0.0100
## [191,] -0.000092599868 0.008141939   0.00000000            0 0.0064
## [192,] -0.001550660708 0.016453987   0.00000000            0 0.0148
## [193,] -0.002427598716 0.020134408   0.00000000            0 0.0212
## [194,] -0.000265933322 0.010791372   0.00000000            0 0.0096
## [195,] -0.001159172612 0.015102321   0.00000000            0 0.0124
## [196,] -0.003392018602 0.027235576   0.00000000            0 0.0240
## [197,] -0.000598168782 0.008410615   0.00000000            0 0.0084
## [198,] -0.001596173806 0.019703456   0.00000000            0 0.0160
## [199,] -0.004345241957 0.041853253   0.00000000            0 0.0216
## [200,] -0.000804285267 0.009694092   0.00000000            0 0.0116
## [201,] -0.000629721061 0.016742453   0.00000000            0 0.0100
## [202,] -0.001609756559 0.014727084   0.00000000            0 0.0164
## [203,] -0.002224708528 0.022528658   0.00000000            0 0.0204
## [204,] -0.001264913222 0.015732057   0.00000000            0 0.0136
## [205,] -0.000618481355 0.010879643   0.00000000            0 0.0060
## [206,] -0.001026264696 0.012127034   0.00000000            0 0.0116
## [207,] -0.001275021542 0.014656490   0.00000000            0 0.0124
## [208,] -0.002644942881 0.020778979   0.00000000            0 0.0208
## [209,] -0.000922493356 0.011404384   0.00000000            0 0.0108
## [210,] -0.000772856550 0.010450643   0.00000000            0 0.0100
## [211,] -0.000213112732 0.004547820   0.00000000            0 0.0052
## [212,] -0.000144996776 0.002920611   0.00000000            0 0.0032
## [213,] -0.000985951030 0.011875989   0.00000000            0 0.0112
## [214,] -0.001153393420 0.012441197   0.00000000            0 0.0120
## [215,] -0.000266936163 0.013188477   0.00000000            0 0.0088
## [216,] -0.004213807068 0.027695766  -0.06049490            0 0.0300
## [217,] -0.005249281667 0.030861139  -0.08951090            0 0.0380
## [218,] -0.001343879479 0.015220153   0.00000000            0 0.0148
## [219,] -0.000525460197 0.006917387   0.00000000            0 0.0084
## [220,] -0.003347366025 0.032292219   0.00000000            0 0.0212
## [221,] -0.000342310578 0.014132439   0.00000000            0 0.0080
## [222,] -0.001186662786 0.012954979   0.00000000            0 0.0124
## [223,]  0.000386531762 0.029549778   0.00000000            0 0.0072
## [224,] -0.002928408768 0.026360799   0.00000000            0 0.0212
## [225,] -0.020173348091 0.156453510  -0.12090822            0 0.0352
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## [491,] -0.001220692628 0.014710536   0.00000000            0 0.0108
## [492,] -0.001703387205 0.016755934   0.00000000            0 0.0160
## [493,] -0.000702220473 0.010405005   0.00000000            0 0.0100
## [494,] -0.000557977449 0.011732295   0.00000000            0 0.0072
## [495,] -0.001331713086 0.015729311   0.00000000            0 0.0112
## [496,] -0.001275963739 0.013395032   0.00000000            0 0.0116
## [497,] -0.000840571692 0.017253737   0.00000000            0 0.0120
## [498,] -0.001159554206 0.014589274   0.00000000            0 0.0116
## [499,] -0.000558606319 0.007335529   0.00000000            0 0.0080
## [500,] -0.001361832333 0.012945146   0.00000000            0 0.0152
## [501,] -0.002301646445 0.021125463   0.00000000            0 0.0176
## [502,] -0.004799247267 0.033788022  -0.05912012            0 0.0324
## [503,] -0.000748444498 0.009215419   0.00000000            0 0.0120
## [504,] -0.006288226022 0.034013739  -0.11868835            0 0.0424
## [505,] -0.002516701387 0.023177473   0.00000000            0 0.0212
## [506,] -0.000889277346 0.011896885   0.00000000            0 0.0124
## [507,] -0.000558417744 0.021611387   0.00000000            0 0.0104
## [508,] -0.001282436994 0.014694072   0.00000000            0 0.0136
## [509,] -0.002202550787 0.020807719   0.00000000            0 0.0172
## [510,] -0.003815130459 0.065851278   0.00000000            0 0.0160
## [511,] -0.000450630374 0.009801785   0.00000000            0 0.0072
## [512,] -0.000738166366 0.009830656   0.00000000            0 0.0084
## [513,] -0.001936506898 0.020192717   0.00000000            0 0.0156
## [514,] -0.000797321198 0.011677112   0.00000000            0 0.0108
## [515,] -0.000560361380 0.008502790   0.00000000            0 0.0092
## [516,] -0.001540996179 0.016337600   0.00000000            0 0.0144
## [517,] -0.002354014771 0.022085179   0.00000000            0 0.0192
## [518,] -0.000185525538 0.018298939   0.00000000            0 0.0064
## [519,] -0.001260143952 0.012593858   0.00000000            0 0.0140
## [520,] -0.001037709638 0.011238347   0.00000000            0 0.0104
## [521,] -0.002103514177 0.040226554   0.00000000            0 0.0132
## [522,] -0.000765533546 0.011105289   0.00000000            0 0.0072
## [523,] -0.001701402050 0.014821152   0.00000000            0 0.0180
## [524,] -0.003901715556 0.027307111  -0.04586726            0 0.0300
## [525,] -0.001426918856 0.014030567   0.00000000            0 0.0132
## [526,] -0.002371332403 0.020118757   0.00000000            0 0.0200
## [527,] -0.000858208566 0.009938438   0.00000000            0 0.0104
## [528,] -0.000778052423 0.010843947   0.00000000            0 0.0092
## [529,] -0.001379554261 0.014250732   0.00000000            0 0.0140
## [530,] -0.000261019648 0.021980693   0.00000000            0 0.0104
## [531,] -0.000932992153 0.017158412   0.00000000            0 0.0144
## [532,] -0.001071924522 0.012829936   0.00000000            0 0.0092
## [533,] -0.002602051900 0.023298605   0.00000000            0 0.0212
## [534,] -0.003358744695 0.059252787   0.00000000            0 0.0156
## [535,] -0.000816480437 0.010190205   0.00000000            0 0.0080
## [536,] -0.000313896899 0.024806237   0.00000000            0 0.0080
## [537,] -0.002858744729 0.023377719   0.00000000            0 0.0228
## [538,] -0.002806381183 0.023046451   0.00000000            0 0.0204
## [539,] -0.000827845732 0.012616610   0.00000000            0 0.0092
## [540,] -0.001390230809 0.014993866   0.00000000            0 0.0136
## [541,] -0.001961347922 0.017111743   0.00000000            0 0.0180
## [542,] -0.000876292473 0.018788566   0.00000000            0 0.0116
## [543,] -0.001367868988 0.014226749   0.00000000            0 0.0140
## [544,] -0.004011499971 0.033148373   0.00000000            0 0.0244
## [545,] -0.002929618555 0.026934991   0.00000000            0 0.0200
## [546,] -0.001081594485 0.012605509   0.00000000            0 0.0132
## [547,] -0.002654969262 0.021903333   0.00000000            0 0.0252
## [548,] -0.002715179096 0.020971956   0.00000000            0 0.0212
## [549,] -0.001198256304 0.017016433   0.00000000            0 0.0136
## [550,] -0.001744314876 0.017641266   0.00000000            0 0.0144
## [551,] -0.000321507667 0.007001099   0.00000000            0 0.0060
## [552,] -0.003211307509 0.025216325   0.00000000            0 0.0240
## [553,] -0.001819611307 0.016803011   0.00000000            0 0.0204
## [554,] -0.001147897155 0.012526218   0.00000000            0 0.0120
## [555,] -0.000443507752 0.015402845   0.00000000            0 0.0088
## [556,] -0.001077368049 0.012470528   0.00000000            0 0.0108
## [557,] -0.001030969669 0.013552104   0.00000000            0 0.0116
## [558,] -0.001759724870 0.032956237   0.00000000            0 0.0096
## [559,] -0.000483469314 0.008224478   0.00000000            0 0.0068
## [560,] -0.000817124746 0.011430166   0.00000000            0 0.0068
## [561,] -0.002499698371 0.024787223   0.00000000            0 0.0196
## [562,] -0.000761113444 0.010817446   0.00000000            0 0.0072
## [563,] -0.001351464297 0.016176986   0.00000000            0 0.0120
## [564,] -0.000792379139 0.011385051   0.00000000            0 0.0108
## [565,] -0.001511233216 0.017234270   0.00000000            0 0.0128
## [566,] -0.000985536798 0.011890582   0.00000000            0 0.0104
## [567,] -0.001514995980 0.019698414   0.00000000            0 0.0108
## [568,] -0.000784102125 0.009825488   0.00000000            0 0.0092
## [569,] -0.001111623518 0.013990311   0.00000000            0 0.0108
## [570,] -0.000838932196 0.022068366   0.00000000            0 0.0120
## [571,] -0.000772167022 0.010567922   0.00000000            0 0.0088
## [572,] -0.000925033438 0.010140514   0.00000000            0 0.0132
## [573,] -0.001720551496 0.015739949   0.00000000            0 0.0160
## [574,] -0.001828174842 0.016880108   0.00000000            0 0.0176
## [575,] -0.000896729260 0.011836839   0.00000000            0 0.0104
## [576,] -0.001232049794 0.012530837   0.00000000            0 0.0120
## [577,] -0.001713802851 0.017275499   0.00000000            0 0.0152
## [578,] -0.001584481425 0.015988393   0.00000000            0 0.0148
## [579,] -0.000841557679 0.010757122   0.00000000            0 0.0100
## [580,] -0.000535540306 0.006621653   0.00000000            0 0.0092
## [581,] -0.002684828932 0.025645459   0.00000000            0 0.0184
## [582,] -0.000970050551 0.011801142   0.00000000            0 0.0100
## [583,] -0.000575391884 0.008962500   0.00000000            0 0.0092
## [584,] -0.001277469875 0.017611904   0.00000000            0 0.0120
## [585,] -0.003249180320 0.032134346   0.00000000            0 0.0216
## [586,] -0.000868206528 0.011077124   0.00000000            0 0.0124
## [587,] -0.001047120561 0.012617718   0.00000000            0 0.0092
## [588,] -0.000849437370 0.012258413   0.00000000            0 0.0092
## [589,] -0.002576938446 0.021942021   0.00000000            0 0.0200
## [590,] -0.000766092753 0.010511929   0.00000000            0 0.0112
## [591,] -0.000806342282 0.010287107   0.00000000            0 0.0096
## [592,] -0.000790504621 0.009676200   0.00000000            0 0.0104
## [593,] -0.001705982426 0.017222286   0.00000000            0 0.0156
## [594,] -0.001814351938 0.020034140   0.00000000            0 0.0148
## [595,] -0.001086221070 0.011100966   0.00000000            0 0.0136
## [596,] -0.000490645582 0.006699115   0.00000000            0 0.0076
## [597,] -0.003858049531 0.032742077   0.00000000            0 0.0228
## [598,] -0.002238752957 0.018415889   0.00000000            0 0.0204
## [599,] -0.000707416354 0.012984304   0.00000000            0 0.0080
## [600,] -0.002126280827 0.017963663   0.00000000            0 0.0200
## [601,] -0.001532635573 0.015291233   0.00000000            0 0.0152
## [602,] -0.000954199632 0.013595414   0.00000000            0 0.0092
## [603,] -0.000704995630 0.009715644   0.00000000            0 0.0108
## [604,] -0.001660404449 0.016752035   0.00000000            0 0.0156
## [605,] -0.000374041618 0.008825640   0.00000000            0 0.0088
## [606,] -0.001413006959 0.025662920   0.00000000            0 0.0108
## [607,]  0.000386092152 0.023953922   0.00000000            0 0.0084
## [608,] -0.000537746421 0.007704036   0.00000000            0 0.0064
## [609,] -0.001438324819 0.015404619   0.00000000            0 0.0140
## [610,] -0.000617746195 0.008165568   0.00000000            0 0.0100
## [611,] -0.000880857035 0.010466872   0.00000000            0 0.0092
## [612,] -0.000571764021 0.008127769   0.00000000            0 0.0084
## [613,] -0.001156237762 0.011897470   0.00000000            0 0.0136
## [614,] -0.000807315152 0.010034944   0.00000000            0 0.0096
## [615,] -0.000912287447 0.011501060   0.00000000            0 0.0100
## [616,] -0.000514392498 0.007278279   0.00000000            0 0.0076
## [617,] -0.001726120721 0.019517495   0.00000000            0 0.0164
## [618,] -0.000799046814 0.011730642   0.00000000            0 0.0080
## [619,] -0.001256839343 0.011586832   0.00000000            0 0.0148
## [620,] -0.000363197568 0.006362618   0.00000000            0 0.0080
## [621,] -0.000963594095 0.013202593   0.00000000            0 0.0112
## [622,] -0.001190645436 0.012741106   0.00000000            0 0.0128
## [623,] -0.000450509879 0.010188536   0.00000000            0 0.0072
## [624,] -0.002440603872 0.020433566   0.00000000            0 0.0204
## [625,] -0.002093768462 0.019700447   0.00000000            0 0.0180
## [626,] -0.001268629928 0.014018842   0.00000000            0 0.0124
## [627,] -0.000483179399 0.007244052   0.00000000            0 0.0060
## [628,] -0.000919775236 0.013172804   0.00000000            0 0.0124
## [629,] -0.000609287378 0.011068640   0.00000000            0 0.0072
## [630,] -0.001178071331 0.013224623   0.00000000            0 0.0108
## [631,] -0.000639882736 0.010127778   0.00000000            0 0.0096
## [632,] -0.000920448358 0.011733652   0.00000000            0 0.0108
## [633,] -0.001425429991 0.016710647   0.00000000            0 0.0148
## [634,] -0.000863141052 0.012597563   0.00000000            0 0.0100
## [635,] -0.001329900434 0.013962215   0.00000000            0 0.0140
## [636,] -0.001779362346 0.019229715   0.00000000            0 0.0172
## [637,] -0.002009985451 0.021885448   0.00000000            0 0.0152
## [638,] -0.000588283445 0.008034087   0.00000000            0 0.0088
## [639,] -0.001564336486 0.018729597   0.00000000            0 0.0140
## [640,] -0.000718906334 0.008339499   0.00000000            0 0.0100
## [641,] -0.001757729430 0.019993950   0.00000000            0 0.0148
## [642,] -0.001005875018 0.011951154   0.00000000            0 0.0120
## [643,] -0.001417063600 0.014078560   0.00000000            0 0.0160
## [644,] -0.001820325327 0.016826487   0.00000000            0 0.0180
## [645,] -0.002644775156 0.022488744   0.00000000            0 0.0216
## [646,] -0.003031699589 0.024276112   0.00000000            0 0.0220
## [647,] -0.000629336097 0.009066464   0.00000000            0 0.0088
## [648,] -0.001648728944 0.015258437   0.00000000            0 0.0164
## [649,] -0.002108373889 0.019920762   0.00000000            0 0.0156
## [650,] -0.001545951474 0.013911093   0.00000000            0 0.0164
## [651,] -0.000953268125 0.012534074   0.00000000            0 0.0100
## [652,] -0.000717691981 0.015177087   0.00000000            0 0.0116
## [653,] -0.000761395094 0.010224604   0.00000000            0 0.0092
## [654,] -0.000963111741 0.012128174   0.00000000            0 0.0112
## [655,] -0.000527329228 0.007770202   0.00000000            0 0.0084
## [656,] -0.000420030057 0.010349193   0.00000000            0 0.0084
## [657,] -0.002948874966 0.028209621   0.00000000            0 0.0196
## [658,]  0.000370056242 0.023222474   0.00000000            0 0.0084
## [659,] -0.001149045079 0.015567084   0.00000000            0 0.0124
## [660,] -0.000645965780 0.007931202   0.00000000            0 0.0092
## [661,] -0.000953618339 0.011966187   0.00000000            0 0.0128
## [662,] -0.000633722618 0.011166534   0.00000000            0 0.0084
## [663,] -0.001834698393 0.016063532   0.00000000            0 0.0172
## [664,] -0.000500243685 0.009375228   0.00000000            0 0.0080
## [665,] -0.001868028735 0.025428884   0.00000000            0 0.0172
## [666,] -0.000905886167 0.010886668   0.00000000            0 0.0120
## [667,] -0.000800623373 0.011099380   0.00000000            0 0.0096
## [668,] -0.000771397926 0.010000676   0.00000000            0 0.0088
## [669,] -0.001396403587 0.016489083   0.00000000            0 0.0124
## [670,] -0.001655279929 0.015792704   0.00000000            0 0.0164

4.5 Fit the NPB model with ozone and temperature, excluding race/ethnicity

Because race/ethnicity might be on the causal pathway (mediator), we want to see if anything shows up when we exclude those variables from the model

priors.npb <- priors.npb.24

#' Exposures
colnames(X.scaled)
##  [1] "mean_pm"             "mean_o3"             "mean_temp"          
##  [4] "pct_tree_cover"      "pct_impervious"      "mean_aadt_intensity"
##  [7] "dist_m_tri"          "dist_m_npl"          "dist_m_waste_site"  
## [10] "dist_m_major_emit"   "dist_m_cafo"         "dist_m_mine_well"   
## [13] "cvd_rate_adj"        "res_rate_adj"        "violent_crime_rate" 
## [16] "property_crime_rate" "pct_less_hs"         "pct_unemp"          
## [19] "pct_limited_eng"     "pct_hh_pov"          "pct_poc"
#' Covariates
colnames(W.scaled2)
##  [1] "lat"            "lon"            "lat_lon_int"    "latina_re"     
##  [5] "black_re"       "other_re"       "ed_no_hs"       "ed_hs"         
##  [9] "ed_aa"          "ed_4yr"         "low_bmi"        "ovwt_bmi"      
## [13] "obese_bmi"      "concep_spring"  "concep_summer"  "concep_fall"   
## [17] "concep_2010"    "concep_2011"    "concep_2012"    "concep_2013"   
## [21] "maternal_age"   "any_smoker"     "smokeSH"        "mean_cpss"     
## [25] "mean_epsd"      "male"           "days_to_peapod"
# fit.npb4 <- npb(niter = 5000, nburn = 2500, X = X.scaled, Y = Y, W = W.scaled2[,-c(4:6)],
#                scaleY = TRUE,
#                priors = priors.npb, interact = TRUE, XWinteract = TRUE)
# save(fit.npb4, file = here::here("Results", "NPB_Adiposity_v4a.2.rdata"))

load(here::here("Results", "NPB_Adiposity_v4a.2.rdata"))
npb.sum4 <- summary(fit.npb4)

4.5.1 First, main effect regression coefficients with PIPs

rownames(npb.sum4$main.effects) <- colnames(X.scaled)
npb.sum4$main.effects
##                     Posterior Mean         SD 95% CI Lower 95% CI Upper    PIP
## mean_pm               -0.010729658 0.05655652  -0.16237261   0.08479285 0.2704
## mean_o3               -0.026837965 0.08139926  -0.25192835   0.07785339 0.3452
## mean_temp             -0.021281728 0.07047256  -0.23587895   0.06986070 0.3164
## pct_tree_cover        -0.008791935 0.05659104  -0.15881790   0.10628675 0.2860
## pct_impervious        -0.013974122 0.05455793  -0.16094311   0.05231081 0.2728
## mean_aadt_intensity    0.013137539 0.06718301  -0.07642895   0.24337509 0.2544
## dist_m_tri            -0.009996501 0.05598899  -0.15666476   0.10753410 0.2852
## dist_m_npl            -0.004519011 0.05142667  -0.12632889   0.11463303 0.2480
## dist_m_waste_site      0.028700543 0.10128321  -0.08273024   0.37373023 0.2940
## dist_m_major_emit      0.003127463 0.05741171  -0.10783720   0.16639638 0.2512
## dist_m_cafo           -0.017787169 0.10566942  -0.23902691   0.11942903 0.3220
## dist_m_mine_well      -0.034101657 0.08603236  -0.27396469   0.06547282 0.3768
## cvd_rate_adj          -0.023228803 0.07073171  -0.23038729   0.06134876 0.3300
## res_rate_adj          -0.026657334 0.06897587  -0.22825010   0.02910509 0.3124
## violent_crime_rate    -0.013739604 0.05881846  -0.16237261   0.07345125 0.3004
## property_crime_rate   -0.060386776 0.10487118  -0.35042634   0.01751900 0.4640
## pct_less_hs           -0.021194253 0.07087443  -0.22560588   0.07172877 0.3128
## pct_unemp             -0.042408868 0.09237638  -0.31381585   0.02807945 0.3704
## pct_limited_eng        0.001753679 0.06262165  -0.10926476   0.16105352 0.2532
## pct_hh_pov            -0.024603132 0.06953043  -0.22759937   0.04145441 0.3176
## pct_poc               -0.005529783 0.05921470  -0.14275717   0.13180881 0.2752

4.5.3 Interactions

Next, all of the interactions between exposures or between exposures and covariates

npb.sum4$interactions
##        Posterior Mean          SD 95% CI Lower 95% CI Upper    PIP
##   [1,] -0.00048119137 0.008045223  0.000000000            0 0.0104
##   [2,] -0.00048702126 0.007029269  0.000000000            0 0.0116
##   [3,] -0.00166674994 0.013658238  0.000000000            0 0.0196
##   [4,] -0.00545531586 0.028924389 -0.089444959            0 0.0492
##   [5,] -0.00063978078 0.008083385  0.000000000            0 0.0124
##   [6,] -0.00106386287 0.011198299  0.000000000            0 0.0132
##   [7,] -0.00148451058 0.013047494  0.000000000            0 0.0188
##   [8,] -0.00798112481 0.037860238 -0.129016543            0 0.0612
##   [9,] -0.00503666985 0.028284795 -0.082627134            0 0.0436
##  [10,] -0.00243106959 0.017397353 -0.007968193            0 0.0256
##  [11,] -0.00322652731 0.021766631 -0.042412585            0 0.0336
##  [12,] -0.00198905414 0.016471919  0.000000000            0 0.0208
##  [13,] -0.00080887744 0.010125656  0.000000000            0 0.0132
##  [14,] -0.00209805479 0.017962448  0.000000000            0 0.0208
##  [15,] -0.00130335268 0.011314406  0.000000000            0 0.0196
##  [16,] -0.00393736380 0.025383067 -0.062857502            0 0.0384
##  [17,] -0.00391637364 0.025791544 -0.062482524            0 0.0340
##  [18,] -0.00665111849 0.034529992 -0.120563494            0 0.0516
##  [19,] -0.00156704349 0.013393877  0.000000000            0 0.0200
##  [20,] -0.00223178575 0.017832880  0.000000000            0 0.0244
##  [21,] -0.00616446901 0.031653243 -0.106168283            0 0.0536
##  [22,] -0.00095746249 0.010861597  0.000000000            0 0.0168
##  [23,] -0.00106672676 0.010111521  0.000000000            0 0.0152
##  [24,] -0.00043380763 0.007687657  0.000000000            0 0.0104
##  [25,] -0.00330673048 0.022986647 -0.041692982            0 0.0300
##  [26,] -0.00169112518 0.013328089  0.000000000            0 0.0216
##  [27,] -0.00266749914 0.017629197 -0.038554235            0 0.0312
##  [28,] -0.00111251582 0.011619953  0.000000000            0 0.0156
##  [29,] -0.00314114621 0.020694758 -0.040843430            0 0.0320
##  [30,] -0.00127803795 0.014083809  0.000000000            0 0.0184
##  [31,] -0.00055167486 0.008095716  0.000000000            0 0.0064
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## [548,] -0.00721302156 0.033840049 -0.124174890            0 0.0612
## [549,] -0.00431709761 0.027997211 -0.061449842            0 0.0356
## [550,] -0.00246654521 0.024941150  0.000000000            0 0.0220
## [551,] -0.00132695094 0.013006843  0.000000000            0 0.0152
## [552,] -0.00206960517 0.018005621  0.000000000            0 0.0240
## [553,] -0.00327002247 0.023866221 -0.034969077            0 0.0288
## [554,] -0.00281469372 0.039988114  0.000000000            0 0.0216
## [555,] -0.00122510584 0.019814101  0.000000000            0 0.0200
## [556,] -0.00097897249 0.010258888  0.000000000            0 0.0148
## [557,] -0.00285935421 0.023386695  0.000000000            0 0.0232
## [558,] -0.00212106949 0.017741842 -0.019131442            0 0.0276
## [559,] -0.00174914428 0.016469467  0.000000000            0 0.0220
## [560,] -0.00151011633 0.014150324  0.000000000            0 0.0188
## [561,] -0.00354026496 0.032115502 -0.027219724            0 0.0276
## [562,] -0.00148819085 0.014327986  0.000000000            0 0.0196
## [563,] -0.00253401551 0.024003676  0.000000000            0 0.0256
## [564,] -0.00197396347 0.015242318  0.000000000            0 0.0232
## [565,] -0.00260022088 0.019708538  0.000000000            0 0.0244
## [566,] -0.00113939311 0.011918514  0.000000000            0 0.0160
## [567,] -0.00289184099 0.019244241 -0.038168487            0 0.0308
## [568,] -0.00395865532 0.025094125 -0.068952463            0 0.0356
## [569,] -0.00277514274 0.020439110 -0.028645649            0 0.0272
## [570,] -0.00309401446 0.019648364 -0.051676725            0 0.0336
## [571,] -0.00156982733 0.014158729  0.000000000            0 0.0192
## [572,] -0.00127633642 0.012303285  0.000000000            0 0.0184
## [573,] -0.00151110294 0.013149747  0.000000000            0 0.0216
## [574,] -0.00163424351 0.017088552  0.000000000            0 0.0184
## [575,] -0.00170573609 0.020986399  0.000000000            0 0.0204
## [576,] -0.00207382581 0.019104489  0.000000000            0 0.0240
## [577,] -0.00321711674 0.021005148 -0.048508074            0 0.0340
## [578,] -0.00389049535 0.049102805  0.000000000            0 0.0240
## [579,] -0.00190886699 0.015625828  0.000000000            0 0.0204
## [580,] -0.00059904449 0.017169471  0.000000000            0 0.0156
## [581,] -0.00381856284 0.029503421 -0.051486534            0 0.0336
## [582,] -0.00457279095 0.034002415 -0.048585205            0 0.0328
## [583,] -0.00151410448 0.013361719  0.000000000            0 0.0164
## [584,] -0.00199343995 0.015761241  0.000000000            0 0.0228
## [585,] -0.00237611194 0.017770083 -0.009995880            0 0.0260
## [586,] -0.00161017480 0.013730629  0.000000000            0 0.0204
## [587,] -0.00304414880 0.027698675 -0.017839771            0 0.0272
## [588,] -0.00460116629 0.027353808 -0.074403884            0 0.0408
## [589,] -0.00308960629 0.028755014 -0.003944801            0 0.0264
## [590,] -0.00199093585 0.018829748  0.000000000            0 0.0236
## [591,] -0.00518301719 0.031991704 -0.076896086            0 0.0424
## [592,] -0.00342034014 0.022882234 -0.050067850            0 0.0348
## [593,] -0.00294923529 0.022660120 -0.026239090            0 0.0276
## [594,] -0.00284720702 0.022051500 -0.011404877            0 0.0268
## [595,] -0.00138593304 0.013370020  0.000000000            0 0.0216
## [596,] -0.00526230147 0.031846448 -0.081470141            0 0.0428
## [597,] -0.00399274861 0.026553005 -0.062784358            0 0.0368
## [598,] -0.00288192077 0.035078322  0.000000000            0 0.0220
## [599,] -0.00111446120 0.012073254  0.000000000            0 0.0180
## [600,] -0.00166724473 0.017733823  0.000000000            0 0.0176
## [601,] -0.00154951245 0.013868289  0.000000000            0 0.0172
## [602,] -0.00149159931 0.012916873  0.000000000            0 0.0192
## [603,] -0.00061978245 0.013792800  0.000000000            0 0.0148
## [604,] -0.00167525301 0.016509908  0.000000000            0 0.0200
## [605,] -0.00252221789 0.018608595 -0.032649990            0 0.0304
## [606,] -0.00092665733 0.010448469  0.000000000            0 0.0176
## [607,] -0.00275538808 0.019644227 -0.031776000            0 0.0288
## [608,] -0.00119008952 0.014280135  0.000000000            0 0.0200
## [609,] -0.00229584052 0.016494117 -0.025877812            0 0.0280
## [610,] -0.00165894301 0.012351968  0.000000000            0 0.0232
## [611,] -0.00150334198 0.014380522  0.000000000            0 0.0172
## [612,] -0.00083266095 0.009688698  0.000000000            0 0.0132
## [613,] -0.00230672211 0.019634993  0.000000000            0 0.0232
## [614,] -0.00263388833 0.020243890 -0.021617901            0 0.0268
## [615,] -0.00189603104 0.014432426  0.000000000            0 0.0248
## [616,] -0.00144527629 0.013830045  0.000000000            0 0.0192
## [617,] -0.00170053532 0.014621710  0.000000000            0 0.0224
## [618,] -0.00250493759 0.017592111 -0.021224474            0 0.0268
## [619,] -0.00109546631 0.011028798  0.000000000            0 0.0140
## [620,] -0.00292306551 0.021682542 -0.021200346            0 0.0276
## [621,] -0.00211480201 0.017484106  0.000000000            0 0.0240
## [622,] -0.00268287146 0.019356395 -0.033006411            0 0.0292
## [623,] -0.00228958578 0.018638406  0.000000000            0 0.0264
## [624,] -0.00116502658 0.013146405  0.000000000            0 0.0164
## [625,] -0.00380697675 0.027592428 -0.048875897            0 0.0336
## [626,] -0.00208820120 0.016606256  0.000000000            0 0.0212
## [627,] -0.00107201172 0.016511179  0.000000000            0 0.0164
## [628,] -0.00165090182 0.014483010  0.000000000            0 0.0208
## [629,] -0.00436859709 0.038445543 -0.044380882            0 0.0344
## [630,] -0.00176428094 0.016268684  0.000000000            0 0.0220
## [631,] -0.00188606908 0.016179771  0.000000000            0 0.0196
## [632,] -0.00214854062 0.016416958  0.000000000            0 0.0252
## [633,] -0.00236898182 0.017459860  0.000000000            0 0.0232
## [634,] -0.00143486738 0.013197803  0.000000000            0 0.0188
## [635,] -0.00181214899 0.019457166  0.000000000            0 0.0212
## [636,] -0.00147866102 0.012490484  0.000000000            0 0.0196
## [637,] -0.00341157020 0.029211622 -0.032385440            0 0.0280
## [638,] -0.00248444947 0.020274788  0.000000000            0 0.0236
## [639,] -0.00179998552 0.014639412  0.000000000            0 0.0208
## [640,] -0.00116791694 0.010924227  0.000000000            0 0.0188
## [641,] -0.00443585435 0.030272189 -0.055935412            0 0.0352
## [642,] -0.00382575534 0.023669909 -0.059860983            0 0.0396
## [643,] -0.00127622506 0.013611424  0.000000000            0 0.0136
## [644,] -0.00405354816 0.026354089 -0.062647867            0 0.0336
## [645,] -0.00227521512 0.018189124  0.000000000            0 0.0244
## [646,] -0.00208390084 0.015563957 -0.013509518            0 0.0272
## [647,] -0.00085190876 0.009492997  0.000000000            0 0.0128
## [648,] -0.00145461188 0.014695583  0.000000000            0 0.0184
## [649,] -0.00113459948 0.011365716  0.000000000            0 0.0204
## [650,] -0.00213269416 0.017081027  0.000000000            0 0.0204
## [651,] -0.00083279051 0.009305455  0.000000000            0 0.0140
## [652,] -0.00063441528 0.013326402  0.000000000            0 0.0136
## [653,] -0.00239601608 0.020556473 -0.014379893            0 0.0264
## [654,] -0.00130905350 0.013854010  0.000000000            0 0.0172
## [655,] -0.00110282953 0.011011849  0.000000000            0 0.0136
## [656,] -0.00083550548 0.016387311  0.000000000            0 0.0132
## [657,] -0.00174620941 0.015824471  0.000000000            0 0.0172
## [658,] -0.00134441660 0.013102996  0.000000000            0 0.0188
## [659,] -0.00206025271 0.018231867  0.000000000            0 0.0200
## [660,] -0.00153727349 0.014064347  0.000000000            0 0.0204
## [661,] -0.00261284838 0.020652608 -0.024360252            0 0.0272
## [662,] -0.00139461299 0.010676269  0.000000000            0 0.0216
## [663,] -0.00173358012 0.014244273  0.000000000            0 0.0216
## [664,] -0.00071029924 0.008786051  0.000000000            0 0.0116
## [665,] -0.00173383551 0.015568045  0.000000000            0 0.0204
## [666,] -0.00179280134 0.015760184  0.000000000            0 0.0228
## [667,] -0.00120789526 0.012724637  0.000000000            0 0.0180
## [668,] -0.00285326867 0.019795421 -0.038349982            0 0.0284
## [669,] -0.00240456655 0.020517498  0.000000000            0 0.0228
## [670,] -0.00233098927 0.018802880  0.000000000            0 0.0236
## [671,] -0.00144873534 0.012512066  0.000000000            0 0.0196
## [672,] -0.00162160390 0.013440288  0.000000000            0 0.0244
## [673,] -0.00159688104 0.015809480  0.000000000            0 0.0212
## [674,] -0.00252490953 0.019754665 -0.028795728            0 0.0284
## [675,] -0.00082687906 0.008963115  0.000000000            0 0.0140
## [676,] -0.00084457847 0.010011871  0.000000000            0 0.0152
## [677,] -0.00193206621 0.016400310  0.000000000            0 0.0228
## [678,] -0.00155947716 0.013741649  0.000000000            0 0.0208
## [679,] -0.00294403065 0.022454101 -0.021815892            0 0.0280
## [680,] -0.00209000513 0.019487588  0.000000000            0 0.0244
## [681,] -0.00213420964 0.017476269  0.000000000            0 0.0228
## [682,] -0.00095526267 0.010816389  0.000000000            0 0.0176
## [683,] -0.00205626027 0.015543067  0.000000000            0 0.0248
## [684,] -0.00110853113 0.010328979  0.000000000            0 0.0172
## [685,] -0.00242527161 0.025079297  0.000000000            0 0.0252
## [686,] -0.00136083117 0.012218031  0.000000000            0 0.0188
## [687,] -0.00290518686 0.019687206 -0.043782692            0 0.0296
## [688,] -0.00225613927 0.017804357  0.000000000            0 0.0244
## [689,] -0.00350993669 0.025312849 -0.041051562            0 0.0280
## [690,] -0.00474115669 0.030491634 -0.070227870            0 0.0408
## [691,] -0.00085850923 0.009330100  0.000000000            0 0.0148
## [692,] -0.00293139965 0.019901881 -0.036489883            0 0.0284
## [693,] -0.00230119307 0.018613455  0.000000000            0 0.0236
## [694,] -0.00360758594 0.032042388 -0.035702531            0 0.0300
## [695,] -0.00153751596 0.014940602  0.000000000            0 0.0200
## [696,] -0.00118483769 0.012940051  0.000000000            0 0.0160
## [697,] -0.00132900114 0.012502399  0.000000000            0 0.0200
## [698,] -0.00185745250 0.037649980  0.000000000            0 0.0204
## [699,] -0.00073628831 0.008541453  0.000000000            0 0.0124
## [700,] -0.00185840025 0.018428784  0.000000000            0 0.0180
## [701,] -0.00345492628 0.030569414 -0.020786599            0 0.0292
## [702,]  0.00024092563 0.026823887  0.000000000            0 0.0176
## [703,] -0.00198113632 0.016219654  0.000000000            0 0.0248
## [704,] -0.00098065978 0.012097749  0.000000000            0 0.0156
## [705,] -0.00176462847 0.017002212  0.000000000            0 0.0216
## [706,] -0.00127266598 0.013055069  0.000000000            0 0.0184
## [707,] -0.00208265351 0.015532531 -0.004198962            0 0.0272
## [708,] -0.00126459912 0.011347460  0.000000000            0 0.0160
## [709,] -0.00348040559 0.049559008 -0.009563184            0 0.0268
## [710,] -0.00187968484 0.014173136  0.000000000            0 0.0228
## [711,] -0.00128407689 0.011284334  0.000000000            0 0.0196
## [712,] -0.00214307349 0.015418050 -0.009810182            0 0.0260
## [713,] -0.00284893621 0.020974023 -0.020655030            0 0.0268
## [714,] -0.00272767710 0.018302132 -0.040609288            0 0.0312

5 Linear models for each predictor

5.1 Screening the exposures

None of the exposures had a PIP > 0.5. Here I’m going to loop through some linear regression models to see if anything shows up here. Remember that the exposure and covariates have all been scaled.

lm_results <- data.frame()

for(i in 1:length(colnames(X.scaled))) {
  lm_df <- as.data.frame(cbind(Y, X.scaled[,i], W.scaled2))
  names(lm_df)[2] <- colnames(X.scaled)[i]
  
  ad_lm <- lm(adiposity ~ ., data = lm_df)
  
  temp <- data.frame(exp = colnames(X.scaled)[i],
                     beta = summary(ad_lm)$coefficients[2,1],
                     beta.se = summary(ad_lm)$coefficients[2,2],
                     p.value = summary(ad_lm)$coefficients[2,4])
  temp$lcl <- temp$beta - 1.96*temp$beta.se
  temp$ucl <- temp$beta + 1.96*temp$beta.se
  lm_results <- bind_rows(lm_results, temp)
  rm(temp)
}

lm_results
write_csv(lm_results, here::here("Results", "LM_Effects_Adiposity_v4.csv"))

5.2 Linear model for distance to waste sites

lm_df <- as.data.frame(cbind(Y, X.scaled, W.scaled2))

ad_waste_lm <- lm(adiposity ~ dist_m_waste_site + 
                    lat + lon + lat_lon_int +
                    latina_re + black_re + other_re + 
                    ed_no_hs + ed_hs + ed_aa + ed_4yr + 
                    low_bmi + ovwt_bmi + obese_bmi + 
                    concep_spring + concep_summer + concep_fall +
                    concep_2010 + concep_2011 + concep_2012 + concep_2013 +
                    maternal_age + any_smoker + smokeSH + 
                    mean_cpss + mean_epsd + male + days_to_peapod,
                    data = lm_df)

summary(ad_waste_lm)
## 
## Call:
## lm(formula = adiposity ~ dist_m_waste_site + lat + lon + lat_lon_int + 
##     latina_re + black_re + other_re + ed_no_hs + ed_hs + ed_aa + 
##     ed_4yr + low_bmi + ovwt_bmi + obese_bmi + concep_spring + 
##     concep_summer + concep_fall + concep_2010 + concep_2011 + 
##     concep_2012 + concep_2013 + maternal_age + any_smoker + smokeSH + 
##     mean_cpss + mean_epsd + male + days_to_peapod, data = lm_df)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -9.1152 -2.6385 -0.1678  2.7592 15.5462 
## 
## Coefficients:
##                    Estimate Std. Error t value      Pr(>|t|)    
## (Intercept)        10.02150    3.90254   2.568        0.0104 *  
## dist_m_waste_site   0.36281    0.15149   2.395        0.0169 *  
## lat                12.72052  148.21325   0.086        0.9316    
## lon                -5.73270   70.63195  -0.081        0.9353    
## lat_lon_int        15.09494  178.21522   0.085        0.9325    
## latina_re          -0.48057    0.40192  -1.196        0.2322    
## black_re           -0.27689    0.43874  -0.631        0.5282    
## other_re           -0.87609    0.57642  -1.520        0.1290    
## ed_no_hs            1.23866    0.65067   1.904        0.0573 .  
## ed_hs               1.07560    0.58154   1.850        0.0648 .  
## ed_aa               0.81041    0.51063   1.587        0.1129    
## ed_4yr              0.07400    0.42583   0.174        0.8621    
## low_bmi            -0.42315    0.80718  -0.524        0.6003    
## ovwt_bmi            0.52044    0.34122   1.525        0.1276    
## obese_bmi           1.24425    0.38806   3.206        0.0014 ** 
## concep_spring       0.29517    0.39971   0.738        0.4605    
## concep_summer       0.13378    0.39414   0.339        0.7344    
## concep_fall         0.03868    0.39069   0.099        0.9212    
## concep_2010        -0.55100    3.90233  -0.141        0.8878    
## concep_2011        -1.11020    3.90475  -0.284        0.7762    
## concep_2012        -1.36997    3.89964  -0.351        0.7255    
## concep_2013        -1.04232    3.90481  -0.267        0.7896    
## maternal_age        0.79576    0.18829   4.226 0.00002669215 ***
## any_smoker         -0.88965    0.53394  -1.666        0.0961 .  
## smokeSH            -0.09976    0.37929  -0.263        0.7926    
## mean_cpss          -0.06078    0.16639  -0.365        0.7150    
## mean_epsd          -0.19513    0.16928  -1.153        0.2494    
## male               -1.37099    0.27394  -5.005 0.00000069768 ***
## days_to_peapod      0.82688    0.13914   5.943 0.00000000429 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.773 on 751 degrees of freedom
## Multiple R-squared:  0.1402, Adjusted R-squared:  0.1082 
## F-statistic: 4.375 on 28 and 751 DF,  p-value: 0.000000000001403
plot(ad_waste_lm)
## Warning: not plotting observations with leverage one:
##   1

5.3 Linear model for respiratory hospitalization rates

lm_df <- as.data.frame(cbind(Y, X.scaled, W.scaled2))

ad_res_lm <- lm(adiposity ~ res_rate_adj + 
                    lat + lon + lat_lon_int +
                    latina_re + black_re + other_re + 
                    ed_no_hs + ed_hs + ed_aa + ed_4yr + 
                    low_bmi + ovwt_bmi + obese_bmi + 
                    concep_spring + concep_summer + concep_fall +
                    concep_2010 + concep_2011 + concep_2012 + concep_2013 +
                    maternal_age + any_smoker + smokeSH + 
                    mean_cpss + mean_epsd + male + days_to_peapod,
                    data = lm_df)

summary(ad_res_lm)
## 
## Call:
## lm(formula = adiposity ~ res_rate_adj + lat + lon + lat_lon_int + 
##     latina_re + black_re + other_re + ed_no_hs + ed_hs + ed_aa + 
##     ed_4yr + low_bmi + ovwt_bmi + obese_bmi + concep_spring + 
##     concep_summer + concep_fall + concep_2010 + concep_2011 + 
##     concep_2012 + concep_2013 + maternal_age + any_smoker + smokeSH + 
##     mean_cpss + mean_epsd + male + days_to_peapod, data = lm_df)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -8.7234 -2.5753 -0.2042  2.7269 16.1631 
## 
## Coefficients:
##                 Estimate Std. Error t value      Pr(>|t|)    
## (Intercept)      9.67278    3.90877   2.475       0.01356 *  
## res_rate_adj    -0.24964    0.15140  -1.649       0.09960 .  
## lat             36.76972  148.72945   0.247       0.80480    
## lon            -17.28087   70.88017  -0.244       0.80745    
## lat_lon_int     44.14802  178.83348   0.247       0.80508    
## latina_re       -0.38383    0.40356  -0.951       0.34185    
## black_re        -0.19174    0.43981  -0.436       0.66298    
## other_re        -0.81865    0.57851  -1.415       0.15746    
## ed_no_hs         1.31937    0.65663   2.009       0.04486 *  
## ed_hs            1.15845    0.58646   1.975       0.04860 *  
## ed_aa            0.94161    0.51282   1.836       0.06673 .  
## ed_4yr           0.13362    0.42564   0.314       0.75367    
## low_bmi         -0.50970    0.80895  -0.630       0.52884    
## ovwt_bmi         0.47288    0.34205   1.382       0.16723    
## obese_bmi        1.26674    0.38909   3.256       0.00118 ** 
## concep_spring    0.31816    0.40032   0.795       0.42700    
## concep_summer    0.11014    0.39513   0.279       0.78053    
## concep_fall      0.04729    0.39147   0.121       0.90387    
## concep_2010     -0.33604    3.90881  -0.086       0.93151    
## concep_2011     -0.86851    3.91105  -0.222       0.82432    
## concep_2012     -1.16914    3.90637  -0.299       0.76480    
## concep_2013     -0.83812    3.91148  -0.214       0.83039    
## maternal_age     0.76831    0.18806   4.086 0.00004870493 ***
## any_smoker      -0.86685    0.53535  -1.619       0.10582    
## smokeSH         -0.09518    0.38007  -0.250       0.80233    
## mean_cpss       -0.04247    0.16639  -0.255       0.79861    
## mean_epsd       -0.19821    0.16980  -1.167       0.24346    
## male            -1.32203    0.27511  -4.805 0.00000186532 ***
## days_to_peapod   0.82938    0.13942   5.949 0.00000000414 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.781 on 751 degrees of freedom
## Multiple R-squared:  0.1368, Adjusted R-squared:  0.1046 
## F-statistic: 4.251 on 28 and 751 DF,  p-value: 0.000000000004589
plot(ad_res_lm)
## Warning: not plotting observations with leverage one:
##   1

5.4 Linear model for property crime rates

lm_df <- as.data.frame(cbind(Y, X.scaled, W.scaled2))

ad_pcrime_lm <- lm(adiposity ~ property_crime_rate + 
                    lat + lon + lat_lon_int +
                    latina_re + black_re + other_re + 
                    ed_no_hs + ed_hs + ed_aa + ed_4yr + 
                    low_bmi + ovwt_bmi + obese_bmi + 
                    concep_spring + concep_summer + concep_fall +
                    concep_2010 + concep_2011 + concep_2012 + concep_2013 +
                    maternal_age + any_smoker + smokeSH + 
                    mean_cpss + mean_epsd + male + days_to_peapod,
                    data = lm_df)

summary(ad_pcrime_lm)
## 
## Call:
## lm(formula = adiposity ~ property_crime_rate + lat + lon + lat_lon_int + 
##     latina_re + black_re + other_re + ed_no_hs + ed_hs + ed_aa + 
##     ed_4yr + low_bmi + ovwt_bmi + obese_bmi + concep_spring + 
##     concep_summer + concep_fall + concep_2010 + concep_2011 + 
##     concep_2012 + concep_2013 + maternal_age + any_smoker + smokeSH + 
##     mean_cpss + mean_epsd + male + days_to_peapod, data = lm_df)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -8.6783 -2.6161 -0.1684  2.7626 15.8124 
## 
## Coefficients:
##                      Estimate Std. Error t value      Pr(>|t|)    
## (Intercept)           9.65291    3.90266   2.473       0.01360 *  
## property_crime_rate  -0.31479    0.13972  -2.253       0.02455 *  
## lat                  31.91270  148.29287   0.215       0.82967    
## lon                 -14.93929   70.67019  -0.211       0.83264    
## lat_lon_int          38.29701  178.30884   0.215       0.83000    
## latina_re            -0.46827    0.40192  -1.165       0.24435    
## black_re             -0.29343    0.43940  -0.668       0.50446    
## other_re             -0.93457    0.57731  -1.619       0.10590    
## ed_no_hs              1.19286    0.65058   1.834       0.06712 .  
## ed_hs                 1.07542    0.58181   1.848       0.06494 .  
## ed_aa                 0.91635    0.51063   1.795       0.07313 .  
## ed_4yr                0.18710    0.42523   0.440       0.66007    
## low_bmi              -0.46686    0.80730  -0.578       0.56324    
## ovwt_bmi              0.46817    0.34145   1.371       0.17074    
## obese_bmi             1.25965    0.38829   3.244       0.00123 ** 
## concep_spring         0.32470    0.39966   0.812       0.41680    
## concep_summer         0.14151    0.39434   0.359       0.71980    
## concep_fall           0.02365    0.39096   0.060       0.95179    
## concep_2010          -0.18066    3.90305  -0.046       0.96309    
## concep_2011          -0.71684    3.90537  -0.184       0.85441    
## concep_2012          -1.03992    3.90058  -0.267       0.78984    
## concep_2013          -0.72418    3.90556  -0.185       0.85295    
## maternal_age          0.77043    0.18770   4.104 0.00004496165 ***
## any_smoker           -0.86307    0.53440  -1.615       0.10672    
## smokeSH              -0.10116    0.37946  -0.267       0.78985    
## mean_cpss            -0.03802    0.16586  -0.229       0.81874    
## mean_epsd            -0.20551    0.16917  -1.215       0.22481    
## male                 -1.40426    0.27486  -5.109 0.00000041128 ***
## days_to_peapod        0.82385    0.13921   5.918 0.00000000495 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.775 on 751 degrees of freedom
## Multiple R-squared:  0.1395, Adjusted R-squared:  0.1074 
## F-statistic: 4.348 on 28 and 751 DF,  p-value: 0.000000000001819
plot(ad_pcrime_lm)
## Warning: not plotting observations with leverage one:
##   1

5.5 Linear model for %unemployed rates

lm_df <- as.data.frame(cbind(Y, X.scaled, W.scaled2))

ad_unemp_lm <- lm(adiposity ~ pct_unemp + 
                    lat + lon + lat_lon_int +
                    latina_re + black_re + other_re + 
                    ed_no_hs + ed_hs + ed_aa + ed_4yr + 
                    low_bmi + ovwt_bmi + obese_bmi + 
                    concep_spring + concep_summer + concep_fall +
                    concep_2010 + concep_2011 + concep_2012 + concep_2013 +
                    maternal_age + any_smoker + smokeSH + 
                    mean_cpss + mean_epsd + male + days_to_peapod,
                    data = lm_df)

summary(ad_unemp_lm)
## 
## Call:
## lm(formula = adiposity ~ pct_unemp + lat + lon + lat_lon_int + 
##     latina_re + black_re + other_re + ed_no_hs + ed_hs + ed_aa + 
##     ed_4yr + low_bmi + ovwt_bmi + obese_bmi + concep_spring + 
##     concep_summer + concep_fall + concep_2010 + concep_2011 + 
##     concep_2012 + concep_2013 + maternal_age + any_smoker + smokeSH + 
##     mean_cpss + mean_epsd + male + days_to_peapod, data = lm_df)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -8.6136 -2.5739 -0.1227  2.6643 15.9796 
## 
## Coefficients:
##                 Estimate Std. Error t value      Pr(>|t|)    
## (Intercept)      9.66018    3.90718   2.472      0.013641 *  
## pct_unemp       -0.27813    0.15209  -1.829      0.067843 .  
## lat             18.84591  148.40739   0.127      0.898984    
## lon             -8.68304   70.72418  -0.123      0.902319    
## lat_lon_int     22.61179  178.44698   0.127      0.899200    
## latina_re       -0.29709    0.40929  -0.726      0.468151    
## black_re        -0.09939    0.44480  -0.223      0.823243    
## other_re        -0.80122    0.57866  -1.385      0.166583    
## ed_no_hs         1.32492    0.65577   2.020      0.043695 *  
## ed_hs            1.19286    0.58775   2.030      0.042755 *  
## ed_aa            0.97771    0.51414   1.902      0.057602 .  
## ed_4yr           0.19854    0.42625   0.466      0.641502    
## low_bmi         -0.41917    0.80868  -0.518      0.604377    
## ovwt_bmi         0.48223    0.34170   1.411      0.158581    
## obese_bmi        1.29104    0.38955   3.314      0.000963 ***
## concep_spring    0.29460    0.40051   0.736      0.462232    
## concep_summer    0.11011    0.39493   0.279      0.780471    
## concep_fall      0.04963    0.39131   0.127      0.899106    
## concep_2010     -0.39542    3.90747  -0.101      0.919421    
## concep_2011     -0.91640    3.90959  -0.234      0.814740    
## concep_2012     -1.21936    3.90492  -0.312      0.754928    
## concep_2013     -0.85571    3.90990  -0.219      0.826821    
## maternal_age     0.74830    0.18780   3.985 0.00007418007 ***
## any_smoker      -0.93043    0.53505  -1.739      0.082455 .  
## smokeSH         -0.08158    0.38005  -0.215      0.830094    
## mean_cpss       -0.03983    0.16616  -0.240      0.810619    
## mean_epsd       -0.19942    0.16960  -1.176      0.240031    
## male            -1.35414    0.27429  -4.937 0.00000097868 ***
## days_to_peapod   0.83228    0.13939   5.971 0.00000000364 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.779 on 751 degrees of freedom
## Multiple R-squared:  0.1375, Adjusted R-squared:  0.1054 
## F-statistic: 4.277 on 28 and 751 DF,  p-value: 0.000000000003591
plot(ad_unemp_lm)
## Warning: not plotting observations with leverage one:
##   1